---
OA_place: repository
OA_type: green
_id: '22163'
abstract:
- lang: eng
text: "For a field F and integers d and k, a set A ⊆ Fd is called k-nearly orthogonal
if its\r\nmembers are non-self-orthogonal and every k + 1 vectors of A include
an orthogonal pair.\r\nWe prove that for every prime p there exists some δ = δ(p)>
0, such that for every field\r\nF of characteristic p and for all integers k ≥
2 and d ≥ k, there exists a k-nearly orthogonal\r\nset of at least dδ·k/ logk
vectors of Fd. The size of the set is optimal up to the logk term\r\nin the exponent.
We further prove two extensions of this result. In the first, we provide a\r\nlarge
set A of non-self-orthogonal vectors of Fd such that for every two subsets of
A of\r\nsize k+1 each, some vector of one of the subsets is orthogonal to some
vector of the other.\r\nIn the second extension, every k + 1 vectors of the produced
set A include ℓ + 1 pairwise\r\northogonal vectors for an arbitrary fixed integer
1 ≤ ℓ ≤ k. The proofs involve probabilistic\r\nand spectral arguments and the
hypergraph container method"
article_number: '114373'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Ishay
full_name: Haviv, Ishay
last_name: Haviv
- first_name: Sam
full_name: Mattheus, Sam
last_name: Mattheus
- first_name: Aleksa
full_name: Milojević, Aleksa
last_name: Milojević
- first_name: Yuval
full_name: Wigderson, Yuval
id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
last_name: Wigderson
citation:
ama: Haviv I, Mattheus S, Milojević A, Wigderson Y. Larger nearly orthogonal sets
over finite fields. Discrete Mathematics. 2025;348(4). doi:10.1016/j.disc.2024.114373
apa: Haviv, I., Mattheus, S., Milojević, A., & Wigderson, Y. (2025). Larger
nearly orthogonal sets over finite fields. Discrete Mathematics. Elsevier.
https://doi.org/10.1016/j.disc.2024.114373
chicago: Haviv, Ishay, Sam Mattheus, Aleksa Milojević, and Yuval Wigderson. “Larger
Nearly Orthogonal Sets over Finite Fields.” Discrete Mathematics. Elsevier,
2025. https://doi.org/10.1016/j.disc.2024.114373.
ieee: I. Haviv, S. Mattheus, A. Milojević, and Y. Wigderson, “Larger nearly orthogonal
sets over finite fields,” Discrete Mathematics, vol. 348, no. 4. Elsevier,
2025.
ista: Haviv I, Mattheus S, Milojević A, Wigderson Y. 2025. Larger nearly orthogonal
sets over finite fields. Discrete Mathematics. 348(4), 114373.
mla: Haviv, Ishay, et al. “Larger Nearly Orthogonal Sets over Finite Fields.” Discrete
Mathematics, vol. 348, no. 4, 114373, Elsevier, 2025, doi:10.1016/j.disc.2024.114373.
short: I. Haviv, S. Mattheus, A. Milojević, Y. Wigderson, Discrete Mathematics 348
(2025).
das_tickbox: '1'
date_created: 2026-06-29T10:53:05Z
date_published: 2025-04-01T00:00:00Z
date_updated: 2026-07-14T08:17:17Z
day: '01'
doi: 10.1016/j.disc.2024.114373
extern: '1'
external_id:
arxiv:
- '2404.01057'
fulldoi: https://doi.org/10.1016/j.disc.2024.114373
intvolume: ' 348'
issue: '4'
keyword:
- Nearly orthogonal sets
- Ramsey theory
- Finite fields
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'https://doi.org/10.48550/arXiv.2404.01057 '
month: '04'
oa: 1
oa_version: Preprint
publication: Discrete Mathematics
publication_identifier:
issn:
- 0012-365X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Larger nearly orthogonal sets over finite fields
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 348
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22168'
abstract:
- lang: eng
text: "Let us say that a graph G is Ramsey for a tuple (H1, ... , Hr) of graphs
if every r-colouring\r\nof the edges of G contains a monochromatic copy of Hi
in colour i, for some i ∈ [[r]].\r\nA famous conjecture of Kohayakawa and Kreuter,
extending seminal work of Rödl and\r\nRucinski, predicts the threshold at which
the binomial random graph ´ Gn,p becomes Ramsey\r\nfor (H1, ... , Hr) asymptotically
almost surely.\r\nIn this paper, we resolve the Kohayakawa–Kreuter conjecture
for almost all tuples of\r\ngraphs. Moreover, we reduce its validity to the truth
of a certain deterministic statement,\r\nwhich is a clear necessary condition
for the conjecture to hold. All of our results actually hold in greater generality,
when one replaces the graphs H1, ... , Hr by finite families\r\nH1, ... , Hr.
Additionally, we pose a natural (deterministic) graph-partitioning conjecture,\r\nwhich
we believe to be of independent interest, and whose resolution would imply the\r\nKohayakawa–Kreuter
conjecture."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: EDEN
full_name: KUPERWASSER, EDEN
last_name: KUPERWASSER
- first_name: WOJCIECH
full_name: SAMOTIJ, WOJCIECH
last_name: SAMOTIJ
- first_name: Yuval
full_name: Wigderson, Yuval
id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
last_name: Wigderson
citation:
ama: KUPERWASSER E, SAMOTIJ W, Wigderson Y. On the Kohayakawa–Kreuter conjecture.
Mathematical Proceedings of the Cambridge Philosophical Society. 2025;178(3):293-320.
doi:10.1017/s0305004125000143
apa: KUPERWASSER, E., SAMOTIJ, W., & Wigderson, Y. (2025). On the Kohayakawa–Kreuter
conjecture. Mathematical Proceedings of the Cambridge Philosophical Society.
Cambridge University Press. https://doi.org/10.1017/s0305004125000143
chicago: KUPERWASSER, EDEN, WOJCIECH SAMOTIJ, and Yuval Wigderson. “On the Kohayakawa–Kreuter
Conjecture.” Mathematical Proceedings of the Cambridge Philosophical Society.
Cambridge University Press, 2025. https://doi.org/10.1017/s0305004125000143.
ieee: E. KUPERWASSER, W. SAMOTIJ, and Y. Wigderson, “On the Kohayakawa–Kreuter conjecture,”
Mathematical Proceedings of the Cambridge Philosophical Society, vol. 178,
no. 3. Cambridge University Press, pp. 293–320, 2025.
ista: KUPERWASSER E, SAMOTIJ W, Wigderson Y. 2025. On the Kohayakawa–Kreuter conjecture.
Mathematical Proceedings of the Cambridge Philosophical Society. 178(3), 293–320.
mla: KUPERWASSER, EDEN, et al. “On the Kohayakawa–Kreuter Conjecture.” Mathematical
Proceedings of the Cambridge Philosophical Society, vol. 178, no. 3, Cambridge
University Press, 2025, pp. 293–320, doi:10.1017/s0305004125000143.
short: E. KUPERWASSER, W. SAMOTIJ, Y. Wigderson, Mathematical Proceedings of the
Cambridge Philosophical Society 178 (2025) 293–320.
date_created: 2026-06-29T10:55:00Z
date_published: 2025-04-28T00:00:00Z
date_updated: 2026-07-14T08:38:08Z
day: '28'
doi: 10.1017/s0305004125000143
extern: '1'
external_id:
arxiv:
- '2307.16611'
fulldoi: https://doi.org/10.1017/s0305004125000143
intvolume: ' 178'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2307.16611
mathsc:
- 05C80
- 05C55
- 05D10
month: '04'
oa: 1
oa_version: Preprint
page: 293-320
publication: Mathematical Proceedings of the Cambridge Philosophical Society
publication_identifier:
eissn:
- 1469-8064
issn:
- 0305-0041
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the Kohayakawa–Kreuter conjecture
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 178
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22172'
abstract:
- lang: eng
text: "A highly influential result of Nikiforov states that if an n-vertex graph
G contains\r\nat least γnh copies of a fixed h-vertex graph H, then G contains
a blowup of H of order\r\nΩγ,H(logn). While the dependence on n is optimal, the
correct dependence on γ is unknown;\r\nall known proofs yield bounds that are
polynomial in γ, but the best known upper bound,\r\ncoming from random graphs,
is only logarithmic in γ. It is a major open problem to narrow\r\nthis gap.\r\nWe
prove that if H is triangle-free, then the logarithmic behavior of the upper bound\r\nis
the truth. That is, under the assumptions above, G contains a blowup of H of order\r\nΩH(logn/log(1/γ)).
This is the first non-trivial instance where the optimal dependence in\r\nNikiforov’s
theorem is known.\r\nAs a consequence, we also prove an upper bound on multicolor
Ramsey numbers of\r\nblowups of triangle-free graphs, proving that the dependence
on the number of colors is\r\npolynomial once the blowup is sufficiently large.
This shows that, from the perspective\r\nof multicolor Ramsey numbers, blowups
of fixed triangle-free graphs behave like bipartite\r\ngraphs."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: António
full_name: Girão, António
last_name: Girão
- first_name: Zach
full_name: Hunter, Zach
last_name: Hunter
- first_name: Yuval
full_name: Wigderson, Yuval
id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
last_name: Wigderson
citation:
ama: Girão A, Hunter Z, Wigderson Y. Blowups of triangle-free graphs. Advances
in Combinatorics. 2025;10. doi:10.19086/aic.2025.10
apa: Girão, A., Hunter, Z., & Wigderson, Y. (2025). Blowups of triangle-free
graphs. Advances in Combinatorics. Alliance of Diamond Open Access Journals.
https://doi.org/10.19086/aic.2025.10
chicago: Girão, António, Zach Hunter, and Yuval Wigderson. “Blowups of Triangle-Free
Graphs.” Advances in Combinatorics. Alliance of Diamond Open Access Journals,
2025. https://doi.org/10.19086/aic.2025.10.
ieee: A. Girão, Z. Hunter, and Y. Wigderson, “Blowups of triangle-free graphs,”
Advances in Combinatorics, vol. 10. Alliance of Diamond Open Access Journals,
2025.
ista: Girão A, Hunter Z, Wigderson Y. 2025. Blowups of triangle-free graphs. Advances
in Combinatorics. 10.
mla: Girão, António, et al. “Blowups of Triangle-Free Graphs.” Advances in Combinatorics,
vol. 10, Alliance of Diamond Open Access Journals, 2025, doi:10.19086/aic.2025.10.
short: A. Girão, Z. Hunter, Y. Wigderson, Advances in Combinatorics 10 (2025).
date_created: 2026-06-29T10:56:44Z
date_published: 2025-12-19T00:00:00Z
date_updated: 2026-07-14T08:50:55Z
day: '19'
doi: 10.19086/aic.2025.10
extern: '1'
external_id:
arxiv:
- '2408.12913'
fulldoi: https://doi.org/10.19086/aic.2025.10
intvolume: ' 10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2408.12913
month: '12'
oa: 1
oa_version: Preprint
publication: Advances in Combinatorics
publication_status: published
publisher: Alliance of Diamond Open Access Journals
quality_controlled: '1'
scopus_import: '1'
status: public
title: Blowups of triangle-free graphs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22181'
abstract:
- lang: eng
text: "A graph G is said to be Ramsey size-linear if r(G, H) = OG(e(H))\r\nfor every
graph H with no isolated vertices. Erdős, Faudree,\r\nRousseau, and Schelp observed
that K4 is not Ramsey size-linear,\r\nbut each of its proper subgraphs is, and
they asked whether there\r\nexist infinitely many such graphs. In this short note,
we answer\r\nthis question in the affirmative"
article_number: '104175'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yuval
full_name: Wigderson, Yuval
id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
last_name: Wigderson
citation:
ama: Wigderson Y. Infinitely many minimally non-Ramsey size-linear graphs. European
Journal of Combinatorics. 2025;128. doi:10.1016/j.ejc.2025.104175
apa: Wigderson, Y. (2025). Infinitely many minimally non-Ramsey size-linear graphs.
European Journal of Combinatorics. Elsevier. https://doi.org/10.1016/j.ejc.2025.104175
chicago: Wigderson, Yuval. “Infinitely Many Minimally Non-Ramsey Size-Linear Graphs.”
European Journal of Combinatorics. Elsevier, 2025. https://doi.org/10.1016/j.ejc.2025.104175.
ieee: Y. Wigderson, “Infinitely many minimally non-Ramsey size-linear graphs,” European
Journal of Combinatorics, vol. 128. Elsevier, 2025.
ista: Wigderson Y. 2025. Infinitely many minimally non-Ramsey size-linear graphs.
European Journal of Combinatorics. 128, 104175.
mla: Wigderson, Yuval. “Infinitely Many Minimally Non-Ramsey Size-Linear Graphs.”
European Journal of Combinatorics, vol. 128, 104175, Elsevier, 2025, doi:10.1016/j.ejc.2025.104175.
short: Y. Wigderson, European Journal of Combinatorics 128 (2025).
date_created: 2026-06-29T10:59:47Z
date_published: 2025-08-01T00:00:00Z
date_updated: 2026-07-14T09:13:09Z
day: '01'
doi: 10.1016/j.ejc.2025.104175
extern: '1'
external_id:
arxiv:
- '2409.05931'
fulldoi: https://doi.org/10.1016/j.ejc.2025.104175
intvolume: ' 128'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: 'https://doi.org/10.48550/arXiv.2409.05931 '
month: '08'
oa: 1
oa_version: Preprint
publication: European Journal of Combinatorics
publication_identifier:
issn:
- 0195-6698
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Infinitely many minimally non-Ramsey size-linear graphs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 128
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22188'
abstract:
- lang: eng
text: "A fundamental fact about bounded-degree graph expanders is that three notions
of expansion—vertex expansion, edge expansion, and spectral expansion—are all
equivalent. In this paper, we study to what extent such a statement is true for
linear-algebraic notions of expansion.\r\n\r\nThere are two well-studied notions
of linear-algebraic expansion, namely, dimension expansion (defined in analogy
to vertex expansion of graphs) and quantum expansion (defined in analogy to spectral
expansion of graphs). Lubotzky and Zelmanov proved that the latter implies the
former. We prove that the converse is false: There are dimension expanders which
are not quantum expanders. This also answers in the negative questions of Lubotzky--Zelmanov
and Dvir--Shpilka on the relation between dimension expansion and Kazhdan's property
T.\r\n\r\nMoreover, this asymmetry is explained by the fact that there are two
distinct linear-algebraic analogues of edge expansion of graphs. The first of
these is quantum edge expansion, which was introduced by Hastings, and which he
proved to be equivalent to quantum expansion. We introduce a new notion, termed
dimension edge expansion, which we prove is equivalent to dimension expansion
and which is implied by quantum edge expansion. Thus, the separation above is
implied by a finer one: dimension edge expansion is strictly weaker than quantum
edge expansion. This new notion also leads to a new, more modular proof of the
Lubotzky--Zelmanov result that quantum expanders are dimension expanders."
article_number: '1'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yinan
full_name: Li, Yinan
last_name: Li
- first_name: Youming
full_name: Qiao, Youming
last_name: Qiao
- first_name: Avi
full_name: Wigderson, Avi
last_name: Wigderson
- first_name: Yuval
full_name: Wigderson, Yuval
id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
last_name: Wigderson
- first_name: Chuanqi
full_name: Zhang, Chuanqi
last_name: Zhang
citation:
ama: Li Y, Qiao Y, Wigderson A, Wigderson Y, Zhang C. On linear-algebraic notions
of expansion. Theory of Computing. 2025;21. doi:10.4086/toc.2025.v021a001
apa: Li, Y., Qiao, Y., Wigderson, A., Wigderson, Y., & Zhang, C. (2025). On
linear-algebraic notions of expansion. Theory of Computing. Theory of Computing
Exchange. https://doi.org/10.4086/toc.2025.v021a001
chicago: Li, Yinan, Youming Qiao, Avi Wigderson, Yuval Wigderson, and Chuanqi Zhang.
“On Linear-Algebraic Notions of Expansion.” Theory of Computing. Theory
of Computing Exchange, 2025. https://doi.org/10.4086/toc.2025.v021a001.
ieee: Y. Li, Y. Qiao, A. Wigderson, Y. Wigderson, and C. Zhang, “On linear-algebraic
notions of expansion,” Theory of Computing, vol. 21. Theory of Computing
Exchange, 2025.
ista: Li Y, Qiao Y, Wigderson A, Wigderson Y, Zhang C. 2025. On linear-algebraic
notions of expansion. Theory of Computing. 21, 1.
mla: Li, Yinan, et al. “On Linear-Algebraic Notions of Expansion.” Theory of
Computing, vol. 21, 1, Theory of Computing Exchange, 2025, doi:10.4086/toc.2025.v021a001.
short: Y. Li, Y. Qiao, A. Wigderson, Y. Wigderson, C. Zhang, Theory of Computing
21 (2025).
date_created: 2026-06-29T12:14:06Z
date_published: 2025-04-12T00:00:00Z
date_updated: 2026-07-14T09:47:56Z
day: '12'
doi: 10.4086/toc.2025.v021a001
extern: '1'
external_id:
arxiv:
- '2212.13154'
fulldoi: https://doi.org/10.4086/toc.2025.v021a001
intvolume: ' 21'
keyword:
- linear algebraic expansion
- quantum expanders
- dimension expanders
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2212.13154
mathsc:
- 05C18
- 68R10
month: '04'
oa: 1
oa_version: Preprint
publication: Theory of Computing
publication_identifier:
issn:
- 1557-2862
publication_status: published
publisher: Theory of Computing Exchange
quality_controlled: '1'
scopus_import: '1'
status: public
title: On linear-algebraic notions of expansion
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22191'
abstract:
- lang: eng
text: "Montgomery and Soundararajan showed that the distribution of ψ(x+H)−ψ(x),
for 0≤ x ≤ N, is approximately normal with mean ∼ H and variance ∼ H log(N/H),
when N\r\nδ ≤ H ≤ N\r\n1−δ\r\n. Their work depends\r\non showing that sums Rk
(h) of k-term singular series are µk (−h log h + Ah)\r\nk/2 + Ok (h\r\nk/2−1/(7k)+ε\r\n),\r\nwhere
A is a constant and µk are the Gaussian moment constants. We study lower-order
terms in the size\r\nof these moments. We conjecture that when k is odd, Rk (h)
≍ h\r\n(k−1)/2\r\n(log h)\r\n(k+1)/2\r\n. We prove an upper\r\nbound with the
correct power of h when k = 3, and prove analogous upper bounds in the function
field\r\nsetting when k = 3 and k = 5. We provide further evidence for this conjecture
in the form of numerical\r\ncomputations."
article_processing_charge: No
article_type: original
author:
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
citation:
ama: Kuperberg VZ. Odd moments in the distribution of primes. Algebra & Number
Theory. 2025;19(4):617-666. doi:10.2140/ant.2025.19.617
apa: Kuperberg, V. Z. (2025). Odd moments in the distribution of primes. Algebra
& Number Theory. Mathematical Sciences Publishers. https://doi.org/10.2140/ant.2025.19.617
chicago: Kuperberg, Vivian Zieve. “Odd Moments in the Distribution of Primes.” Algebra
& Number Theory. Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/ant.2025.19.617.
ieee: V. Z. Kuperberg, “Odd moments in the distribution of primes,” Algebra &
Number Theory, vol. 19, no. 4. Mathematical Sciences Publishers, pp. 617–666,
2025.
ista: Kuperberg VZ. 2025. Odd moments in the distribution of primes. Algebra &
Number Theory. 19(4), 617–666.
mla: Kuperberg, Vivian Zieve. “Odd Moments in the Distribution of Primes.” Algebra
& Number Theory, vol. 19, no. 4, Mathematical Sciences Publishers, 2025,
pp. 617–66, doi:10.2140/ant.2025.19.617.
short: V.Z. Kuperberg, Algebra & Number Theory 19 (2025) 617–666.
date_created: 2026-06-29T12:56:09Z
date_published: 2025-03-24T00:00:00Z
date_updated: 2026-07-14T10:52:02Z
day: '24'
doi: 10.2140/ant.2025.19.617
extern: '1'
external_id:
unknown:
- '2109.03767'
fulldoi: https://doi.org/10.2140/ant.2025.19.617
intvolume: ' 19'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2109.03767
mathsc:
- 11N05
- 11N13
month: '03'
oa: 1
oa_version: Preprint
page: 617-666
publication: Algebra & Number Theory
publication_identifier:
eissn:
- 1944-7833
issn:
- 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Odd moments in the distribution of primes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22195'
abstract:
- lang: eng
text: 'Sums of the singular series constants that appear in the Hardy–Littlewood
k-tuples conjectures have long been studied in connection to the distribution
of primes. We study constrained sums of singular series, where the sum is taken
over sets whose elements are specified modulo r or weighted by smooth functions.
We show that the value of the sum is governed by incidences modulo r of elements
of the set in the case of arithmetic progressions and by pairings of the smooth
functions in the case of weights. These sums shed light on sums of singular series
in other formats. '
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
citation:
ama: Kuperberg VZ. Sums of singular series along arithmetic progressions and with
smooth weights. International Journal of Number Theory. 2025;21(01):53-74.
doi:10.1142/s1793042125500046
apa: Kuperberg, V. Z. (2025). Sums of singular series along arithmetic progressions
and with smooth weights. International Journal of Number Theory. World
Scientific Publishing. https://doi.org/10.1142/s1793042125500046
chicago: Kuperberg, Vivian Zieve. “Sums of Singular Series along Arithmetic Progressions
and with Smooth Weights.” International Journal of Number Theory. World
Scientific Publishing, 2025. https://doi.org/10.1142/s1793042125500046.
ieee: V. Z. Kuperberg, “Sums of singular series along arithmetic progressions and
with smooth weights,” International Journal of Number Theory, vol. 21,
no. 01. World Scientific Publishing, pp. 53–74, 2025.
ista: Kuperberg VZ. 2025. Sums of singular series along arithmetic progressions
and with smooth weights. International Journal of Number Theory. 21(01), 53–74.
mla: Kuperberg, Vivian Zieve. “Sums of Singular Series along Arithmetic Progressions
and with Smooth Weights.” International Journal of Number Theory, vol.
21, no. 01, World Scientific Publishing, 2025, pp. 53–74, doi:10.1142/s1793042125500046.
short: V.Z. Kuperberg, International Journal of Number Theory 21 (2025) 53–74.
date_created: 2026-06-29T12:57:46Z
date_published: 2025-01-01T00:00:00Z
date_updated: 2026-07-14T11:04:58Z
day: '01'
doi: 10.1142/s1793042125500046
extern: '1'
external_id:
arxiv:
- '2301.06095'
fulldoi: https://doi.org/10.1142/s1793042125500046
intvolume: ' 21'
issue: '01'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2301.06095
month: '01'
oa: 1
oa_version: Preprint
page: 53-74
publication: International Journal of Number Theory
publication_identifier:
eissn:
- 1793-7310
issn:
- 1793-0421
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sums of singular series along arithmetic progressions and with smooth weights
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22200'
abstract:
- lang: eng
text: "In Kuperberg and Lal´ın [Forum Math. 34 (2022), pp. 711–747],\r\nthe authors
studied the mean-square of certain sums of the divisor function\r\ndk(f) over
the function field Fq[T] in the limit as q →∞ and related these\r\nsums to integrals
over the ensemble of symplectic matrices, along similar lines\r\nas previous work
of Keating, Rodgers, Roditty-Gershon and Rudnick [Math. Z.\r\n288 (2018), pp.
167–198] for unitary matrices. We present an analogous problem yielding an integral
over the ensemble of orthogonal matrices and pursue\r\na more detailed study of
both the symplectic and orthogonal matrix integrals,\r\nrelating them to symmetric
function theory. The function field results lead to\r\nconjectures concerning
analogous questions over number fields."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
- first_name: Matilde
full_name: Lalín, Matilde
last_name: Lalín
citation:
ama: Kuperberg VZ, Lalín M. Symplectic conjectures for sums of divisor functions
and explorations of an orthogonal regime. Transactions of the American Mathematical
Society, Series B. 2025;12(10):323-370. doi:10.1090/btran/186
apa: Kuperberg, V. Z., & Lalín, M. (2025). Symplectic conjectures for sums of
divisor functions and explorations of an orthogonal regime. Transactions of
the American Mathematical Society, Series B. American Mathematical Society.
https://doi.org/10.1090/btran/186
chicago: Kuperberg, Vivian Zieve, and Matilde Lalín. “Symplectic Conjectures for
Sums of Divisor Functions and Explorations of an Orthogonal Regime.” Transactions
of the American Mathematical Society, Series B. American Mathematical Society,
2025. https://doi.org/10.1090/btran/186.
ieee: V. Z. Kuperberg and M. Lalín, “Symplectic conjectures for sums of divisor
functions and explorations of an orthogonal regime,” Transactions of the American
Mathematical Society, Series B, vol. 12, no. 10. American Mathematical Society,
pp. 323–370, 2025.
ista: Kuperberg VZ, Lalín M. 2025. Symplectic conjectures for sums of divisor functions
and explorations of an orthogonal regime. Transactions of the American Mathematical
Society, Series B. 12(10), 323–370.
mla: Kuperberg, Vivian Zieve, and Matilde Lalín. “Symplectic Conjectures for Sums
of Divisor Functions and Explorations of an Orthogonal Regime.” Transactions
of the American Mathematical Society, Series B, vol. 12, no. 10, American
Mathematical Society, 2025, pp. 323–70, doi:10.1090/btran/186.
short: V.Z. Kuperberg, M. Lalín, Transactions of the American Mathematical Society,
Series B 12 (2025) 323–370.
date_created: 2026-06-29T12:59:46Z
date_published: 2025-03-20T00:00:00Z
date_updated: 2026-07-14T11:24:55Z
day: '20'
doi: 10.1090/btran/186
extern: '1'
external_id:
arxiv:
- '2212.04969'
fulldoi: https://doi.org/10.1090/btran/186
intvolume: ' 12'
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2212.04969
mathsc:
- 11N60
- 05A15
- 11M50
- 11N56
month: '03'
oa: 1
oa_version: Preprint
page: 323-370
publication: Transactions of the American Mathematical Society, Series B
publication_identifier:
issn:
- 2330-0000
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Symplectic conjectures for sums of divisor functions and explorations of an
orthogonal regime
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22199'
abstract:
- lang: eng
text: Kuperberg and Lalín stated some conjectures on the variance of certain sums
of the divisor function dk(n) over number fields, which were inspired by analogous
results over function fields proven by the authors. These problems are related
to certain symplectic matrix integrals. While the function field results can be
directly related to the random matrix integrals, the connection between the random
matrix integrals and the number field results is less direct and involves arithmetic
factors. The goal of this article is to give heuristic arguments for the formulas
of these arithmetic factors.
article_number: e70029
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
- first_name: Matilde
full_name: Lalín, Matilde
last_name: Lalín
citation:
ama: Kuperberg VZ, Lalín M. Arithmetic constants for symplectic variances of the
divisor function. Mathematika. 2025;71(3). doi:10.1112/mtk.70029
apa: Kuperberg, V. Z., & Lalín, M. (2025). Arithmetic constants for symplectic
variances of the divisor function. Mathematika. Wiley. https://doi.org/10.1112/mtk.70029
chicago: Kuperberg, Vivian Zieve, and Matilde Lalín. “Arithmetic Constants for Symplectic
Variances of the Divisor Function.” Mathematika. Wiley, 2025. https://doi.org/10.1112/mtk.70029.
ieee: V. Z. Kuperberg and M. Lalín, “Arithmetic constants for symplectic variances
of the divisor function,” Mathematika, vol. 71, no. 3. Wiley, 2025.
ista: Kuperberg VZ, Lalín M. 2025. Arithmetic constants for symplectic variances
of the divisor function. Mathematika. 71(3), e70029.
mla: Kuperberg, Vivian Zieve, and Matilde Lalín. “Arithmetic Constants for Symplectic
Variances of the Divisor Function.” Mathematika, vol. 71, no. 3, e70029,
Wiley, 2025, doi:10.1112/mtk.70029.
short: V.Z. Kuperberg, M. Lalín, Mathematika 71 (2025).
date_created: 2026-06-29T12:59:16Z
date_published: 2025-05-01T00:00:00Z
date_updated: 2026-07-14T11:20:10Z
day: '01'
doi: 10.1112/mtk.70029
extern: '1'
external_id:
arxiv:
- '2410.17939'
fulldoi: https://doi.org/10.1112/mtk.70029
intvolume: ' 71'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2410.17939
mathsc:
- 11N60
- 05A15
- 11M50
- 11N56
month: '05'
oa: 1
oa_version: Preprint
publication: Mathematika
publication_identifier:
issn:
- 0025-5793
- 2041-7942
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Arithmetic constants for symplectic variances of the divisor function
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 71
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22201'
abstract:
- lang: eng
text: We consider an analog of a conjecture of Montgomery and Soundararajan on the
moments of primes in short intervals in number fields; this analog was discussed
and heuristically derived in a paper of the second author, Rodgers, and Roditty-Gershon.
Adapting work of the first author and Fiorilli in the integer case, we establish
lower bounds on a weighted version of these moments which agree with the conjectured
values.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Régis
full_name: de la Bretèche, Régis
last_name: de la Bretèche
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
citation:
ama: de la Bretèche R, Kuperberg VZ. Lower bounds on weighted moments of primes
in short intervals in number fields. Israel Journal of Mathematics. 2025;267(1):437-461.
doi:10.1007/s11856-024-2711-0
apa: de la Bretèche, R., & Kuperberg, V. Z. (2025). Lower bounds on weighted
moments of primes in short intervals in number fields. Israel Journal of Mathematics.
Springer Nature. https://doi.org/10.1007/s11856-024-2711-0
chicago: Bretèche, Régis de la, and Vivian Zieve Kuperberg. “Lower Bounds on Weighted
Moments of Primes in Short Intervals in Number Fields.” Israel Journal of Mathematics.
Springer Nature, 2025. https://doi.org/10.1007/s11856-024-2711-0.
ieee: R. de la Bretèche and V. Z. Kuperberg, “Lower bounds on weighted moments of
primes in short intervals in number fields,” Israel Journal of Mathematics,
vol. 267, no. 1. Springer Nature, pp. 437–461, 2025.
ista: de la Bretèche R, Kuperberg VZ. 2025. Lower bounds on weighted moments of
primes in short intervals in number fields. Israel Journal of Mathematics. 267(1),
437–461.
mla: de la Bretèche, Régis, and Vivian Zieve Kuperberg. “Lower Bounds on Weighted
Moments of Primes in Short Intervals in Number Fields.” Israel Journal of Mathematics,
vol. 267, no. 1, Springer Nature, 2025, pp. 437–61, doi:10.1007/s11856-024-2711-0.
short: R. de la Bretèche, V.Z. Kuperberg, Israel Journal of Mathematics 267 (2025)
437–461.
date_created: 2026-06-29T13:00:06Z
date_published: 2025-06-01T00:00:00Z
date_updated: 2026-07-14T11:28:49Z
day: '01'
doi: 10.1007/s11856-024-2711-0
extern: '1'
external_id:
arxiv:
- '2305.02662'
fulldoi: https://doi.org/10.1007/s11856-024-2711-0
intvolume: ' 267'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2305.02662
month: '06'
oa: 1
oa_version: Preprint
page: 437-461
publication: Israel Journal of Mathematics
publication_identifier:
eissn:
- 1565-8511
issn:
- 0021-2172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower bounds on weighted moments of primes in short intervals in number fields
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 267
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22203'
abstract:
- lang: eng
text: "We prove near-optimal upper bounds for the oddmoments of the distribution
of coprime residues inshort intervals, confirming a conjecture of Montgomeryand
Vaughan. As an application, we prove near-optimalupper bounds for the average
of the refined singularseries in the Hardy–Littlewood conjectures concerningthe
number of prime \U0001D458-tuples for \U0001D458 odd. The mainnew ingredient is
a near-optimal upper bound for thenumber of solutions to ∑1 ⩽\U0001D456 ⩽\U0001D458\U0001D44E
\U0001D456\U0001D45E\U0001D456∈ ℤ when \U0001D458 is odd,with gcd(\U0001D44E\U0001D456
, \U0001D45E\U0001D456 ) = 1 and restrictions on the size of thenumerators and
denominators, which is of indepen-dent interest."
article_number: e70068
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Thomas F.
full_name: Bloom, Thomas F.
last_name: Bloom
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
citation:
ama: Bloom TF, Kuperberg VZ. Odd moments and adding fractions. Proceedings of
the London Mathematical Society. 2025;131(1). doi:10.1112/plms.70068
apa: Bloom, T. F., & Kuperberg, V. Z. (2025). Odd moments and adding fractions.
Proceedings of the London Mathematical Society. Wiley. https://doi.org/10.1112/plms.70068
chicago: Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.”
Proceedings of the London Mathematical Society. Wiley, 2025. https://doi.org/10.1112/plms.70068.
ieee: T. F. Bloom and V. Z. Kuperberg, “Odd moments and adding fractions,” Proceedings
of the London Mathematical Society, vol. 131, no. 1. Wiley, 2025.
ista: Bloom TF, Kuperberg VZ. 2025. Odd moments and adding fractions. Proceedings
of the London Mathematical Society. 131(1), e70068.
mla: Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.”
Proceedings of the London Mathematical Society, vol. 131, no. 1, e70068,
Wiley, 2025, doi:10.1112/plms.70068.
short: T.F. Bloom, V.Z. Kuperberg, Proceedings of the London Mathematical Society
131 (2025).
date_created: 2026-06-29T13:00:46Z
date_published: 2025-07-01T00:00:00Z
date_updated: 2026-07-14T11:45:18Z
day: '01'
doi: 10.1112/plms.70068
extern: '1'
external_id:
arxiv:
- '2312.09021'
fulldoi: https://doi.org/10.1112/plms.70068
intvolume: ' 131'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2312.09021
mathsc:
- 11N69
- 11N05
- 14G05
month: '07'
oa: 1
oa_version: Preprint
publication: Proceedings of the London Mathematical Society
publication_identifier:
eissn:
- 1460-244X
issn:
- 0024-6115
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Odd moments and adding fractions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 131
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22204'
abstract:
- lang: eng
text: "We study the distribution of consecutive sums of two squares in arithmetic
progressions. We\r\nshow that for any odd squarefree modulus q, any two reduced
congruence classes a1 and a2 mod q,\r\nand any r1,r2 ≥ 1, a positive density of
sums of two squares begin a chain of r1 consecutive sums of\r\ntwo squares, all
of which are a1 mod q, followed immediately by a chain of r2 consecutive sums
of two\r\nsquares, all of which are a2 mod q. This is an analog of the result
of Maynard for the sequence of primes,\r\nshowing that for any reduced congruence
class a mod q and for any r ≥ 1, a positive density of primes\r\nbegin a sequence
of r consecutive primes, all of which are a mod q"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Noam
full_name: Kimmel, Noam
last_name: Kimmel
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
citation:
ama: Kimmel N, Kuperberg VZ. Positive density for consecutive runs of sums of two
squares. Journal of the Institute of Mathematics of Jussieu. 2025;24(5):1995-2046.
doi:10.1017/s1474748025000131
apa: Kimmel, N., & Kuperberg, V. Z. (2025). Positive density for consecutive
runs of sums of two squares. Journal of the Institute of Mathematics of Jussieu.
Cambridge University Press. https://doi.org/10.1017/s1474748025000131
chicago: Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive
Runs of Sums of Two Squares.” Journal of the Institute of Mathematics of Jussieu.
Cambridge University Press, 2025. https://doi.org/10.1017/s1474748025000131.
ieee: N. Kimmel and V. Z. Kuperberg, “Positive density for consecutive runs of sums
of two squares,” Journal of the Institute of Mathematics of Jussieu, vol.
24, no. 5. Cambridge University Press, pp. 1995–2046, 2025.
ista: Kimmel N, Kuperberg VZ. 2025. Positive density for consecutive runs of sums
of two squares. Journal of the Institute of Mathematics of Jussieu. 24(5), 1995–2046.
mla: Kimmel, Noam, and Vivian Zieve Kuperberg. “Positive Density for Consecutive
Runs of Sums of Two Squares.” Journal of the Institute of Mathematics of Jussieu,
vol. 24, no. 5, Cambridge University Press, 2025, pp. 1995–2046, doi:10.1017/s1474748025000131.
short: N. Kimmel, V.Z. Kuperberg, Journal of the Institute of Mathematics of Jussieu
24 (2025) 1995–2046.
date_created: 2026-06-29T13:01:08Z
date_published: 2025-09-01T00:00:00Z
date_updated: 2026-07-14T11:50:36Z
day: '01'
doi: 10.1017/s1474748025000131
extern: '1'
external_id:
arxiv:
- '2406.04174'
fulldoi: https://doi.org/10.1017/s1474748025000131
intvolume: ' 24'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2406.04174
month: '09'
oa: 1
oa_version: Preprint
page: 1995-2046
publication: Journal of the Institute of Mathematics of Jussieu
publication_identifier:
eissn:
- 1475-3030
issn:
- 1474-7480
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Positive density for consecutive runs of sums of two squares
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '22213'
abstract:
- lang: eng
text: Unlike biological active matter that constantly adapt to their environment,
the motors of synthetic active particles are typically agnostic to their surroundings
and merely operate at constant force. Here, we design colloidal active rods capable
of modulating their inner activity in response to crowding, thereby enforcing
a primitive form of quorum sensing interactions. Through experiments, simulations,
and theory we elucidate the impact of these interactions on the phase behavior
of isotropic active matter. We demonstrate that, when conditioned to density,
motility regulation can either lead to an absorbing phase transition, where all
particles freeze their dynamics, or to atypical phase separation, where flat interfaces
supporting a net pressure drop are in mechanical equilibrium. Fully active and
fully arrested particles can then form heterogeneous patterns ruled by the competition
between quorum sensing and mechanical interactions. Beyond the specifics of motile
colloids, we expect our findings to apply broadly to adaptive active matter assembled
from living or synthetic units.
article_number: '031050'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Thibault
full_name: Lefranc, Thibault
last_name: Lefranc
- first_name: Alberto
full_name: Dinelli, Alberto
last_name: Dinelli
- first_name: Carla
full_name: Fernández-Rico, Carla
id: 492def71-6250-11f0-b278-d41dbd241b62
last_name: Fernández-Rico
- first_name: Roel P. A.
full_name: Dullens, Roel P. A.
last_name: Dullens
- first_name: Julien
full_name: Tailleur, Julien
last_name: Tailleur
- first_name: Denis
full_name: Bartolo, Denis
last_name: Bartolo
citation:
ama: Lefranc T, Dinelli A, Fernández-Rico C, Dullens RPA, Tailleur J, Bartolo D.
Synthetic quorum sensing and absorbing phase transitions in colloidal active matter.
Physical Review X. 2025;15(3). doi:10.1103/8csn-71jk
apa: Lefranc, T., Dinelli, A., Fernández-Rico, C., Dullens, R. P. A., Tailleur,
J., & Bartolo, D. (2025). Synthetic quorum sensing and absorbing phase transitions
in colloidal active matter. Physical Review X. American Physical Society.
https://doi.org/10.1103/8csn-71jk
chicago: Lefranc, Thibault, Alberto Dinelli, Carla Fernández-Rico, Roel P. A. Dullens,
Julien Tailleur, and Denis Bartolo. “Synthetic Quorum Sensing and Absorbing Phase
Transitions in Colloidal Active Matter.” Physical Review X. American Physical
Society, 2025. https://doi.org/10.1103/8csn-71jk.
ieee: T. Lefranc, A. Dinelli, C. Fernández-Rico, R. P. A. Dullens, J. Tailleur,
and D. Bartolo, “Synthetic quorum sensing and absorbing phase transitions in colloidal
active matter,” Physical Review X, vol. 15, no. 3. American Physical Society,
2025.
ista: Lefranc T, Dinelli A, Fernández-Rico C, Dullens RPA, Tailleur J, Bartolo D.
2025. Synthetic quorum sensing and absorbing phase transitions in colloidal active
matter. Physical Review X. 15(3), 031050.
mla: Lefranc, Thibault, et al. “Synthetic Quorum Sensing and Absorbing Phase Transitions
in Colloidal Active Matter.” Physical Review X, vol. 15, no. 3, 031050,
American Physical Society, 2025, doi:10.1103/8csn-71jk.
short: T. Lefranc, A. Dinelli, C. Fernández-Rico, R.P.A. Dullens, J. Tailleur, D.
Bartolo, Physical Review X 15 (2025).
date_created: 2026-06-30T06:32:31Z
date_published: 2025-08-22T00:00:00Z
date_updated: 2026-07-15T07:21:38Z
day: '22'
ddc:
- '530'
doi: 10.1103/8csn-71jk
extern: '1'
external_id:
arxiv:
- '2502.13919'
fulldoi: https://doi.org/10.1103/8csn-71jk
has_accepted_license: '1'
intvolume: ' 15'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1103/8csn-71jk
month: '08'
oa: 1
oa_version: Published Version
publication: Physical Review X
publication_identifier:
issn:
- 2160-3308
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Synthetic quorum sensing and absorbing phase transitions in colloidal active
matter
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 15
year: '2025'
...
---
OA_type: closed access
_id: '22214'
abstract:
- lang: eng
text: Highly interconnected percolated networks are interesting structures for materials
with enhanced transport and mechanical properties. While percolated networks of
anisotropic particles have been explored at the nanoscale, achieving highly interconnected
structures at the microscale remains challenging. In this work, we explore the
controlled assembly of rod-like polymer colloids under external fields leading
to reversible quasi-2D networks. By varying voltage and frequency, we modulate
the pore size and thickness of the network. We find that field-driven attractive
interactions enable percolation at lower area fractions than predicted for non-interacting
rods. Monte Carlo simulations incorporating dipolar interactions and electrostatic
boundary conditions confirm the field-induced transition from isotropic to aligned
rod configurations, supporting the emergence of percolated networks. This work
presents a simple and robust approach for assembling reconfigurable colloidal
networks with controlled connectivity, offering new strategies for designing adaptive
soft materials.
article_processing_charge: No
article_type: original
author:
- first_name: José
full_name: Fojo, José
last_name: Fojo
- first_name: Rodolfo
full_name: Subert, Rodolfo
last_name: Subert
- first_name: Laura
full_name: Rodríguez-Arco, Laura
last_name: Rodríguez-Arco
- first_name: Modesto T.
full_name: López-López, Modesto T.
last_name: López-López
- first_name: Marjolein
full_name: Dijkstra, Marjolein
last_name: Dijkstra
- first_name: Carla
full_name: Fernández-Rico, Carla
id: 492def71-6250-11f0-b278-d41dbd241b62
last_name: Fernández-Rico
- first_name: Laura
full_name: Alvarez, Laura
last_name: Alvarez
citation:
ama: Fojo J, Subert R, Rodríguez-Arco L, et al. Field-driven reversible networks
from colloidal rods. Soft Matter. 2025;21(23):4596-4605. doi:10.1039/d5sm00218d
apa: Fojo, J., Subert, R., Rodríguez-Arco, L., López-López, M. T., Dijkstra, M.,
Fernández-Rico, C., & Alvarez, L. (2025). Field-driven reversible networks
from colloidal rods. Soft Matter. Royal Society of Chemistry. https://doi.org/10.1039/d5sm00218d
chicago: Fojo, José, Rodolfo Subert, Laura Rodríguez-Arco, Modesto T. López-López,
Marjolein Dijkstra, Carla Fernández-Rico, and Laura Alvarez. “Field-Driven Reversible
Networks from Colloidal Rods.” Soft Matter. Royal Society of Chemistry,
2025. https://doi.org/10.1039/d5sm00218d.
ieee: J. Fojo et al., “Field-driven reversible networks from colloidal rods,”
Soft Matter, vol. 21, no. 23. Royal Society of Chemistry, pp. 4596–4605,
2025.
ista: Fojo J, Subert R, Rodríguez-Arco L, López-López MT, Dijkstra M, Fernández-Rico
C, Alvarez L. 2025. Field-driven reversible networks from colloidal rods. Soft
Matter. 21(23), 4596–4605.
mla: Fojo, José, et al. “Field-Driven Reversible Networks from Colloidal Rods.”
Soft Matter, vol. 21, no. 23, Royal Society of Chemistry, 2025, pp. 4596–605,
doi:10.1039/d5sm00218d.
short: J. Fojo, R. Subert, L. Rodríguez-Arco, M.T. López-López, M. Dijkstra, C.
Fernández-Rico, L. Alvarez, Soft Matter 21 (2025) 4596–4605.
date_created: 2026-06-30T06:32:50Z
date_published: 2025-06-21T00:00:00Z
date_updated: 2026-07-15T07:37:27Z
day: '21'
doi: 10.1039/d5sm00218d
extern: '1'
external_id:
pmid:
- '40314070'
fulldoi: https://doi.org/10.1039/d5sm00218d
intvolume: ' 21'
issue: '23'
language:
- iso: eng
month: '06'
oa_version: None
page: 4596-4605
pmid: 1
publication: Soft Matter
publication_identifier:
eissn:
- 1744-6848
issn:
- 1744-683X
publication_status: published
publisher: Royal Society of Chemistry
quality_controlled: '1'
scopus_import: '1'
status: public
title: Field-driven reversible networks from colloidal rods
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 21
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '12311'
abstract:
- lang: eng
text: In this note, we prove a formula for the cancellation exponent kv,n between
division polynomials ψn and ϕn associated with a sequence {nP}n∈N of points
on an elliptic curve E defined over a discrete valuation field K. The formula
greatly generalizes the previously known special cases and treats also the case
of non-standard Kodaira types for non-perfect residue fields.
acknowledgement: Silverman, and Paul Voutier for the comments on the earlier version
of this paper. The first author acknowledges the support by Dioscuri programme initiated
by the Max Planck Society, jointly managed with the National Science Centre (Poland),
and mutually funded by the Polish Ministry of Science and Higher Education and the
German Federal Ministry of Education and Research. The second author has been supported
by MIUR (Italy) through PRIN 2017 ‘Geometric, algebraic and analytic methods in
arithmetic’ and has received funding from the European Union's Horizon 2020 research
and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101034413.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Bartosz
full_name: Naskręcki, Bartosz
last_name: Naskręcki
- first_name: Matteo
full_name: Verzobio, Matteo
id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
last_name: Verzobio
orcid: 0000-0002-0854-0306
citation:
ama: 'Naskręcki B, Verzobio M. Common valuations of division polynomials. Proceedings
of the Royal Society of Edinburgh Section A: Mathematics. 2025;155(5):1646-1660.
doi:10.1017/prm.2024.7'
apa: 'Naskręcki, B., & Verzobio, M. (2025). Common valuations of division polynomials.
Proceedings of the Royal Society of Edinburgh Section A: Mathematics. Cambridge
University Press. https://doi.org/10.1017/prm.2024.7'
chicago: 'Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division
Polynomials.” Proceedings of the Royal Society of Edinburgh Section A: Mathematics.
Cambridge University Press, 2025. https://doi.org/10.1017/prm.2024.7.'
ieee: 'B. Naskręcki and M. Verzobio, “Common valuations of division polynomials,”
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol.
155, no. 5. Cambridge University Press, pp. 1646–1660, 2025.'
ista: 'Naskręcki B, Verzobio M. 2025. Common valuations of division polynomials.
Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 155(5),
1646–1660.'
mla: 'Naskręcki, Bartosz, and Matteo Verzobio. “Common Valuations of Division Polynomials.”
Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol.
155, no. 5, Cambridge University Press, 2025, pp. 1646–60, doi:10.1017/prm.2024.7.'
short: 'B. Naskręcki, M. Verzobio, Proceedings of the Royal Society of Edinburgh
Section A: Mathematics 155 (2025) 1646–1660.'
corr_author: '1'
das_tickbox: '0'
date_created: 2023-01-16T11:45:22Z
date_published: 2025-10-01T00:00:00Z
date_updated: 2026-07-16T08:43:40Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/prm.2024.7
ec_funded: 1
external_id:
arxiv:
- '2203.02015'
isi:
- '001174907100001'
file:
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checksum: c5ec6e29aca2fb4533cb95fac409a0b2
content_type: application/pdf
creator: dernst
date_created: 2025-12-30T06:45:47Z
date_updated: 2025-12-30T06:45:47Z
file_id: '20878'
file_name: 2025_ProceedingsRoyalSocEdinburghA_Naskrecki.pdf
file_size: 477624
relation: main_file
success: 1
file_date_updated: 2025-12-30T06:45:47Z
fulldoi: https://doi.org/10.1017/prm.2024.7
has_accepted_license: '1'
intvolume: ' 155'
isi: 1
issue: '5'
keyword:
- Elliptic curves
- Néron models
- division polynomials
- height functions
- discrete valuation rings
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 1646-1660
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: 'Proceedings of the Royal Society of Edinburgh Section A: Mathematics'
publication_identifier:
eissn:
- 1473-7124
issn:
- 0308-2105
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Common valuations of division polynomials
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 155
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20797'
abstract:
- lang: eng
text: Quantum key distribution (QKD) offers a theoretically secure method to share
secret keys, yet practical implementations face challenges due to noise and loss
over long-distance channels. Traditional QKD protocols require extensive noise
compensation, hindering their industrial scalability and lowering the achievable
key rates. Alternative protocols encode logical qubits in noise-resilient states
but at the cost of using many physical qubits, increasing susceptibility to loss
and limiting transmission distance. In this work, we introduce a logical-qubit
encoding that uses antisymmetric Bell states in the continuous photonic degrees
of freedom, frequency and time. By leveraging the continuous space, we overcome
this noise-loss robustness trade-off by minimizing the number of photons per logical
qubit while optimizing the encoding resilience over noise fluctuations. We analyze
the security of our encoding and demonstrate its robustness compared to existing
state-of-the-art protocols. This approach provides a path toward scalable, efficient
QKD implementations under realistic noise conditions.
acknowledgement: We thank B. Baragiola, A. Boubriak, M. Clark, M. Jones, and P. Skrzypczyk
for useful discussions. H.S. acknowledges financial support from EPSRC Quantum Engineering
Centre for Doctoral Training Grant No. EP/SO23607/1. E.L. acknowledges support from
the Engineering and Physical Sciences Research Council (EPSRC) Hub in Quantum Computing
and Simulation (EP/T001062/1). T.S. acknowledges that they received no funding in
support of this research. M.P.S. acknowledges support from the EPSRC Quantum Engineering
Centre for Doctoral Training EP/SO23607/1 and the European Commission through Starting
Grant No. ERC-2018-STG803665 (PEQEM). G.R. acknowledges support from the Royal Commission
for the Exhibition of 1851 through a Research Fellowship, from the European Commission
through Starting Grant No. ERC-2018-STG803665 (PEQEM) and Advanced Grant No. ERC-2020-ADG101021085
(FLQuant), and from EPSRC through Standard Proposal Grant No. EP/X016218/1 (Mono-Squeeze).
article_number: '024072'
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Hannah
full_name: Seabrook, Hannah
last_name: Seabrook
- first_name: Emilien
full_name: Lavie, Emilien
last_name: Lavie
- first_name: Karl T
full_name: Strömberg, Karl T
id: 68011cd2-da32-11ee-a930-b2774c7aba5f
last_name: Strömberg
- first_name: Matthew P.
full_name: Stafford, Matthew P.
last_name: Stafford
- first_name: Giulia
full_name: Rubino, Giulia
last_name: Rubino
citation:
ama: Seabrook H, Lavie E, Strömberg KT, Stafford MP, Rubino G. Surpassing the loss-noise
robustness trade-off in quantum key distribution. Physical Review Applied.
2025;24(2). doi:10.1103/xq2l-r4r7
apa: Seabrook, H., Lavie, E., Strömberg, K. T., Stafford, M. P., & Rubino, G.
(2025). Surpassing the loss-noise robustness trade-off in quantum key distribution.
Physical Review Applied. American Physical Society. https://doi.org/10.1103/xq2l-r4r7
chicago: Seabrook, Hannah, Emilien Lavie, Karl T Strömberg, Matthew P. Stafford,
and Giulia Rubino. “Surpassing the Loss-Noise Robustness Trade-off in Quantum
Key Distribution.” Physical Review Applied. American Physical Society,
2025. https://doi.org/10.1103/xq2l-r4r7.
ieee: H. Seabrook, E. Lavie, K. T. Strömberg, M. P. Stafford, and G. Rubino, “Surpassing
the loss-noise robustness trade-off in quantum key distribution,” Physical
Review Applied, vol. 24, no. 2. American Physical Society, 2025.
ista: Seabrook H, Lavie E, Strömberg KT, Stafford MP, Rubino G. 2025. Surpassing
the loss-noise robustness trade-off in quantum key distribution. Physical Review
Applied. 24(2), 024072.
mla: Seabrook, Hannah, et al. “Surpassing the Loss-Noise Robustness Trade-off in
Quantum Key Distribution.” Physical Review Applied, vol. 24, no. 2, 024072,
American Physical Society, 2025, doi:10.1103/xq2l-r4r7.
short: H. Seabrook, E. Lavie, K.T. Strömberg, M.P. Stafford, G. Rubino, Physical
Review Applied 24 (2025).
das_tickbox: '1'
dataavailabilitystatement: 'The data that support the findings of this article are
openly available at https://github.com/hmis4/SurpassingLNTradeOffQKD; https://github.com/hmis4/SurpassingLNTradeOffQKD/tree/main/DomainEngineering '
date_created: 2025-12-11T10:46:28Z
date_published: 2025-08-29T00:00:00Z
date_updated: 2026-07-16T08:27:32Z
day: '29'
ddc:
- '530'
department:
- _id: OnHo
doi: 10.1103/xq2l-r4r7
external_id:
arxiv:
- '2412.08694'
file:
- access_level: open_access
checksum: 12ddb0414780f65b8e690fe0e6cfb95e
content_type: application/pdf
creator: dernst
date_created: 2025-12-15T09:39:12Z
date_updated: 2025-12-15T09:39:12Z
file_id: '20824'
file_name: 2025_PhysReviewApplied_Seabrook.pdf
file_size: 3028735
relation: main_file
success: 1
file_date_updated: 2025-12-15T09:39:12Z
fulldoi: https://doi.org/10.1103/xq2l-r4r7
has_accepted_license: '1'
intvolume: ' 24'
issue: '2'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
publication: Physical Review Applied
publication_identifier:
eissn:
- 2331-7019
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: no
title: Surpassing the loss-noise robustness trade-off in quantum key distribution
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 24
year: '2025'
...
---
OA_place: publisher
OA_type: diamond
PlanS_conform: '1'
_id: '21244'
abstract:
- lang: eng
text: 'Given a family of varieties over the projective line, we study the density
of fibres that are everywhere locally soluble in the case that components of higher
multiplicity are allowed. We use log geometry to formulate a new sparsity criterion
for the existence of everywhere locally soluble fibres and formulate new conjectures
that generalise previous work of Loughran and Smeets. These conjectures involve
geometric invariants of the associated multiplicity orbifolds on the base of the
fibration in the spirit of Campana. We give evidence for the conjectures by providing
an assortment of bounds using Chebotarev’s theorem and sieve methods, with most
of the evidence involving upper bounds. '
acknowledgement: We are very grateful to Tim Santens for useful conversations and
to the anonymous referees for numerous pertinent remarks. While working on this
paper, Browning was supported by a FWF grant (DOI 10.55776/P32428), Lyczak was supported
by UKRI MR/V021362/1, and Smeets was supported by grant G0B1721N of the Fund for
Scientific Research – Flanders.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Julian
full_name: Lyczak, Julian
last_name: Lyczak
- first_name: Arne
full_name: Smeets, Arne
last_name: Smeets
citation:
ama: Browning TD, Lyczak J, Smeets A. Paucity of rational points on fibrations with
multiple fibres. Algebra & Number Theory. 2025;19(10):2049-2090. doi:10.2140/ant.2025.19.2049
apa: Browning, T. D., Lyczak, J., & Smeets, A. (2025). Paucity of rational points
on fibrations with multiple fibres. Algebra & Number Theory. Mathematical
Sciences Publishers. https://doi.org/10.2140/ant.2025.19.2049
chicago: Browning, Timothy D, Julian Lyczak, and Arne Smeets. “Paucity of Rational
Points on Fibrations with Multiple Fibres.” Algebra & Number Theory.
Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/ant.2025.19.2049.
ieee: T. D. Browning, J. Lyczak, and A. Smeets, “Paucity of rational points on fibrations
with multiple fibres,” Algebra & Number Theory, vol. 19, no. 10. Mathematical
Sciences Publishers, pp. 2049–2090, 2025.
ista: Browning TD, Lyczak J, Smeets A. 2025. Paucity of rational points on fibrations
with multiple fibres. Algebra & Number Theory. 19(10), 2049–2090.
mla: Browning, Timothy D., et al. “Paucity of Rational Points on Fibrations with
Multiple Fibres.” Algebra & Number Theory, vol. 19, no. 10, Mathematical
Sciences Publishers, 2025, pp. 2049–90, doi:10.2140/ant.2025.19.2049.
short: T.D. Browning, J. Lyczak, A. Smeets, Algebra & Number Theory 19 (2025)
2049–2090.
corr_author: '1'
das_tickbox: '0'
date_created: 2026-02-16T15:22:19Z
date_published: 2025-09-05T00:00:00Z
date_updated: 2026-07-16T08:52:36Z
day: '05'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.2140/ant.2025.19.2049
external_id:
arxiv:
- '2310.01135'
file:
- access_level: open_access
checksum: e50a60a4303b81563f7adbcadbe2e986
content_type: application/pdf
creator: dernst
date_created: 2026-02-17T11:56:20Z
date_updated: 2026-02-17T11:56:20Z
file_id: '21300'
file_name: 2025_AlgebraNumberTheory_Browning.pdf
file_size: 1505580
relation: main_file
success: 1
file_date_updated: 2026-02-17T11:56:20Z
fulldoi: https://doi.org/10.2140/ant.2025.19.2049
has_accepted_license: '1'
intvolume: ' 19'
issue: '10'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 2049-2090
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Algebra & Number Theory
publication_identifier:
eissn:
- 1944-7833
issn:
- 1937-0652
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
researchdata_availability: no
status: public
supplementarymaterial: no
title: Paucity of rational points on fibrations with multiple fibres
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 19
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '20850'
abstract:
- lang: eng
text: We provide an estimate for the number of nontrivial integer points on the
Pellian surface t^2 - du^2 = 1 in a bounded region. We give a lower bound on the
size of fundamental solutions for almost all d in a certain class, based on a
recent conjecture of Browning and Wilsch about integer points on log K3 surfaces.
We also obtain an upper bound on the average of class number in this class, assuming
the same conjecture.
- lang: fre
text: "Nous donnons une estimation du nombre de points entiers non triviaux sur
la surface pellienne \r\nt^2 - du^2 = 1 dans une région bornée. Nous établissons
une borne inférieure pour la taille des solutions fondamentales pour presque tout
d appartenant à une certaine classe, en nous fondant sur une conjecture récente
de Browning et Wilsch concernant les points entiers sur les surfaces log K3. Nous
obtenons également une borne supérieure pour la moyenne du nombre de classes dans
cette classe, sous la même hypothèse conjecturale."
acknowledgement: The author would like to thank his supervisor Tim Browning for suggesting
this project and many helpful conversations and useful comments. Moreover, he is
grateful to Jakob Glas, Damaris Schindler, Igor Shparlinski, Matteo Verzobio, Victor
Wang, Florian Wilsch and Shuntaro Yamagishi for taking their time to answer his
questions and their valuable suggestions.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Yijie
full_name: Diao, Yijie
id: 7b7eb4ca-eb2c-11ec-b98b-accec0b20c3b
last_name: Diao
orcid: 0000-0002-4989-5330
citation:
ama: Diao Y. Class numbers and integer points on some Pellian surfaces. Journal
de theorie des nombres de Bordeaux. 2025;37(3):973-988. doi:10.5802/jtnb.1348
apa: Diao, Y. (2025). Class numbers and integer points on some Pellian surfaces.
Journal de Theorie Des Nombres de Bordeaux. Université de Bordeaux. https://doi.org/10.5802/jtnb.1348
chicago: Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.”
Journal de Theorie Des Nombres de Bordeaux. Université de Bordeaux, 2025.
https://doi.org/10.5802/jtnb.1348.
ieee: Y. Diao, “Class numbers and integer points on some Pellian surfaces,” Journal
de theorie des nombres de Bordeaux, vol. 37, no. 3. Université de Bordeaux,
pp. 973–988, 2025.
ista: Diao Y. 2025. Class numbers and integer points on some Pellian surfaces. Journal
de theorie des nombres de Bordeaux. 37(3), 973–988.
mla: Diao, Yijie. “Class Numbers and Integer Points on Some Pellian Surfaces.” Journal
de Theorie Des Nombres de Bordeaux, vol. 37, no. 3, Université de Bordeaux,
2025, pp. 973–88, doi:10.5802/jtnb.1348.
short: Y. Diao, Journal de Theorie Des Nombres de Bordeaux 37 (2025) 973–988.
corr_author: '1'
das_tickbox: '0'
date_created: 2025-12-21T23:01:35Z
date_published: 2025-11-27T00:00:00Z
date_updated: 2026-07-16T08:45:12Z
day: '27'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.5802/jtnb.1348
external_id:
arxiv:
- '2408.03774'
file:
- access_level: open_access
checksum: 67aa0afbc0b5bcbff5341f4d25e6ba20
content_type: application/pdf
creator: dernst
date_created: 2025-12-29T10:05:22Z
date_updated: 2025-12-29T10:05:22Z
file_id: '20861'
file_name: 2025_JTNB_Diao.pdf
file_size: 766196
relation: main_file
success: 1
file_date_updated: 2025-12-29T10:05:22Z
fulldoi: https://doi.org/10.5802/jtnb.1348
has_accepted_license: '1'
intvolume: ' 37'
issue: '3'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nd/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 973-988
publication: Journal de theorie des nombres de Bordeaux
publication_identifier:
eissn:
- 2118-8572
issn:
- 1246-7405
publication_status: published
publisher: Université de Bordeaux
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Class numbers and integer points on some Pellian surfaces
tmp:
image: /image/cc_by_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nd/4.0/legalcode
name: Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)
short: CC BY-ND (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 37
year: '2025'
...
---
OA_place: publisher
OA_type: diamond
_id: '21003'
abstract:
- lang: eng
text: We extend work of Heath-Brown and Salberger, based on the determinant method,
to provide a uniform upper bound for the number of integral points of bounded
height on an affine surface, which are subject to a polynomial congruence condition.
This is applied to get a new uniform bound for points on diagonal quadric surfaces,
and to a problem about the representation of integers as a sum of four unlike
powers.
acknowledgement: "Supported by FWF grant (DOI 10.55776/P36278), Supported by European
Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie
Grant\r\nAgreement No. 101034413."
article_number: '12'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Timothy D
full_name: Browning, Timothy D
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Matteo
full_name: Verzobio, Matteo
id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
last_name: Verzobio
orcid: 0000-0002-0854-0306
citation:
ama: Browning TD, Verzobio M. Counting integer points on affine surfaces with a
side condition. Discrete Analysis. 2025;2025. doi:10.19086/da.143787
apa: 'Browning, T. D., & Verzobio, M. (2025). Counting integer points on affine
surfaces with a side condition. Discrete Analysis. Cambridge: Alliance
of Diamond Open Access Journals. https://doi.org/10.19086/da.143787'
chicago: 'Browning, Timothy D, and Matteo Verzobio. “Counting Integer Points on
Affine Surfaces with a Side Condition.” Discrete Analysis. Cambridge: Alliance
of Diamond Open Access Journals, 2025. https://doi.org/10.19086/da.143787.'
ieee: 'T. D. Browning and M. Verzobio, “Counting integer points on affine surfaces
with a side condition,” Discrete Analysis, vol. 2025. Cambridge: Alliance
of Diamond Open Access Journals, 2025.'
ista: Browning TD, Verzobio M. 2025. Counting integer points on affine surfaces
with a side condition. Discrete Analysis. 2025, 12.
mla: 'Browning, Timothy D., and Matteo Verzobio. “Counting Integer Points on Affine
Surfaces with a Side Condition.” Discrete Analysis, vol. 2025, 12, Cambridge:
Alliance of Diamond Open Access Journals, 2025, doi:10.19086/da.143787.'
short: T.D. Browning, M. Verzobio, Discrete Analysis 2025 (2025).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-01-18T23:02:44Z
date_published: 2025-09-01T00:00:00Z
date_updated: 2026-07-16T08:48:35Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.19086/da.143787
ec_funded: 1
external_id:
arxiv:
- '2408.11453'
file:
- access_level: open_access
checksum: 3d38e850b40f3e1abbfd30073bd4388a
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creator: dernst
date_created: 2026-02-12T07:50:47Z
date_updated: 2026-02-12T07:50:47Z
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file_name: 2025_DiscreteAnalysis_Browning.pdf
file_size: 393625
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fulldoi: https://doi.org/10.19086/da.143787
has_accepted_license: '1'
intvolume: ' 2025'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: bd8a4fdc-d553-11ed-ba76-80a0167441a3
grant_number: P36278
name: Rational curves via function field analytic number theory
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Discrete Analysis
publication_identifier:
eissn:
- 2397-3129
publication_status: published
publisher: 'Cambridge: Alliance of Diamond Open Access Journals'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Counting integer points on affine surfaces with a side condition
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
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volume: 2025
year: '2025'
...
---
OA_place: publisher
OA_type: diamond
_id: '21260'
abstract:
- lang: eng
text: We prove that there does not exist F∈Q[x,y] of degree 4 such that F(Z^2 )=Z
≥0. In particular, this answers a question by John S. Lew and Bjorn Poonen for
quartic polynomials.
acknowledgement: "The first author would like to thank Samir Siksek for introducing
the problem\r\nto him. The material in Section 6 is a result of discussing with
many people, and the second author is very grateful to Tim Browning, Stephanie Chan,
Jakob Glas, Jakub Löwit, Mirko Mauri, Marta Pieropan, Mike Roth, Matteo Verzobio
and Victor Wang for taking the time to answer his questions and for their valuable
suggestions. We thank Tim Browning, Yijie Diao, Ana Marija Vego and the anonymous
referee for their helpful comments.\r\nThe first author was supported by NSERC Discovery
Grant RGPIN-2024-06810. The\r\nsecond author was supported by the NWO Veni Grant
016.Veni.192.047 during his time at\r\nUtrecht University and by a FWF grant (DOI
10.55776/P32428) at the Institute of Science and\r\nTechnology Austria while working
on this paper."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Stanley
full_name: Yao Xiao, Stanley
last_name: Yao Xiao
- first_name: Shuntaro
full_name: Yamagishi, Shuntaro
id: 0c3fbc5c-f7a6-11ec-8d70-9485e75b416b
last_name: Yamagishi
citation:
ama: Yao Xiao S, Yamagishi S. Quartic polynomials in two variables do not represent
all non-negative integers. Journal of the European Mathematical Society.
2025. doi:10.4171/jems/1697
apa: Yao Xiao, S., & Yamagishi, S. (2025). Quartic polynomials in two variables
do not represent all non-negative integers. Journal of the European Mathematical
Society. EMS Press. https://doi.org/10.4171/jems/1697
chicago: Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two
Variables Do Not Represent All Non-Negative Integers.” Journal of the European
Mathematical Society. EMS Press, 2025. https://doi.org/10.4171/jems/1697.
ieee: S. Yao Xiao and S. Yamagishi, “Quartic polynomials in two variables do not
represent all non-negative integers,” Journal of the European Mathematical
Society. EMS Press, 2025.
ista: Yao Xiao S, Yamagishi S. 2025. Quartic polynomials in two variables do not
represent all non-negative integers. Journal of the European Mathematical Society.
mla: Yao Xiao, Stanley, and Shuntaro Yamagishi. “Quartic Polynomials in Two Variables
Do Not Represent All Non-Negative Integers.” Journal of the European Mathematical
Society, EMS Press, 2025, doi:10.4171/jems/1697.
short: S. Yao Xiao, S. Yamagishi, Journal of the European Mathematical Society (2025).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-02-16T16:00:02Z
date_published: 2025-08-06T00:00:00Z
date_updated: 2026-07-16T08:54:37Z
day: '06'
ddc:
- '500'
department:
- _id: TiBr
doi: 10.4171/jems/1697
external_id:
arxiv:
- '2307.05712'
fulldoi: https://doi.org/10.4171/jems/1697
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.4171/JEMS/1697
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P32428
name: New frontiers of the Manin conjecture
publication: Journal of the European Mathematical Society
publication_identifier:
eissn:
- 1435-9863
issn:
- 1435-9855
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
researchdata_availability: no
status: public
supplementarymaterial: no
title: Quartic polynomials in two variables do not represent all non-negative integers
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2025'
...