---
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'
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'
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'
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'
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'
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'
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'
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: repository
OA_type: green
_id: '22190'
abstract:
- lang: eng
text: "We consider the set of \U0001D45A×\U0001D45B matrices with rational entries
having numerator and denominator of size at most H and obtain various upper bounds
on the number of such matrices of a given rank, or with a given determinant, or
a given characteristic polynomial. We also consider similar questions for matrices
whose entries are Egyptian fractions."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Muhammad
full_name: Afifurrahman, Muhammad
last_name: Afifurrahman
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
- first_name: Alina
full_name: Ostafe, Alina
last_name: Ostafe
- first_name: Igor E.
full_name: Shparlinski, Igor E.
last_name: Shparlinski
citation:
ama: Afifurrahman M, Kuperberg VZ, Ostafe A, Shparlinski IE. Statistics of ranks,
determinants and characteristic polynomials of rational matrices. Forum Mathematicum.
2024;37(4). doi:10.1515/forum-2024-0114
apa: Afifurrahman, M., Kuperberg, V. Z., Ostafe, A., & Shparlinski, I. E. (2024).
Statistics of ranks, determinants and characteristic polynomials of rational matrices.
Forum Mathematicum. De Gruyter. https://doi.org/10.1515/forum-2024-0114
chicago: Afifurrahman, Muhammad, Vivian Zieve Kuperberg, Alina Ostafe, and Igor
E. Shparlinski. “Statistics of Ranks, Determinants and Characteristic Polynomials
of Rational Matrices.” Forum Mathematicum. De Gruyter, 2024. https://doi.org/10.1515/forum-2024-0114.
ieee: M. Afifurrahman, V. Z. Kuperberg, A. Ostafe, and I. E. Shparlinski, “Statistics
of ranks, determinants and characteristic polynomials of rational matrices,” Forum
Mathematicum, vol. 37, no. 4. De Gruyter, 2024.
ista: Afifurrahman M, Kuperberg VZ, Ostafe A, Shparlinski IE. 2024. Statistics of
ranks, determinants and characteristic polynomials of rational matrices. Forum
Mathematicum. 37(4).
mla: Afifurrahman, Muhammad, et al. “Statistics of Ranks, Determinants and Characteristic
Polynomials of Rational Matrices.” Forum Mathematicum, vol. 37, no. 4,
De Gruyter, 2024, doi:10.1515/forum-2024-0114.
short: M. Afifurrahman, V.Z. Kuperberg, A. Ostafe, I.E. Shparlinski, Forum Mathematicum
37 (2024).
date_created: 2026-06-29T12:55:47Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2026-07-14T10:48:41Z
doi: 10.1515/forum-2024-0114
extern: '1'
external_id:
arxiv:
- '2401.10086'
intvolume: ' 37'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2401.10086
mathsc:
- 11C20
- 15B36
- 15B52
month: '01'
oa: 1
oa_version: Preprint
publication: Forum Mathematicum
publication_identifier:
eissn:
- 1435-5337
issn:
- 0933-7741
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
scopus_import: '1'
status: public
title: Statistics of ranks, determinants and characteristic polynomials of rational
matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 37
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '22197'
abstract:
- lang: eng
text: "We study the distribution of consecutive sums of two squares\r\nin arithmetic
progressions. If {En}n∈N is the sequence of\r\nsums of two squares in increasing
order, we show that for\r\nany modulus q and any congruence classes a1, a2, a3
mod q\r\nwhich are admissible in the sense that there are solutions\r\nto x2 +
y2 ≡ ai mod q, there exist infinitely many n with\r\nEn+i−1 ≡ ai mod q, for i
=1, 2, 3. We also show that for\r\nany r1, r2 ≥ 1, there exist infinitely many
n with En+i−1 ≡\r\na1 mod q for 1 ≤ i ≤ r1 and En+i−1 ≡ a2 mod q for\r\nr1 +1
≤ i ≤ r1 + r2"
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. Consecutive runs of sums of two squares. Journal
of Number Theory. 2024;264:135-147. doi:10.1016/j.jnt.2024.05.003
apa: Kimmel, N., & Kuperberg, V. Z. (2024). Consecutive runs of sums of two
squares. Journal of Number Theory. Elsevier. https://doi.org/10.1016/j.jnt.2024.05.003
chicago: Kimmel, Noam, and Vivian Zieve Kuperberg. “Consecutive Runs of Sums of
Two Squares.” Journal of Number Theory. Elsevier, 2024. https://doi.org/10.1016/j.jnt.2024.05.003.
ieee: N. Kimmel and V. Z. Kuperberg, “Consecutive runs of sums of two squares,”
Journal of Number Theory, vol. 264. Elsevier, pp. 135–147, 2024.
ista: Kimmel N, Kuperberg VZ. 2024. Consecutive runs of sums of two squares. Journal
of Number Theory. 264, 135–147.
mla: Kimmel, Noam, and Vivian Zieve Kuperberg. “Consecutive Runs of Sums of Two
Squares.” Journal of Number Theory, vol. 264, Elsevier, 2024, pp. 135–47,
doi:10.1016/j.jnt.2024.05.003.
short: N. Kimmel, V.Z. Kuperberg, Journal of Number Theory 264 (2024) 135–147.
date_created: 2026-06-29T12:58:28Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2026-07-14T11:10:45Z
day: '01'
doi: 10.1016/j.jnt.2024.05.003
extern: '1'
external_id:
arxiv:
- '2306.12855'
intvolume: ' 264'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.48550/arXiv.2306.12855
month: '11'
oa_version: Preprint
page: 135-147
publication: Journal of Number Theory
publication_identifier:
issn:
- 0022-314X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Consecutive runs of sums of two squares
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 264
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '22192'
abstract:
- lang: eng
text: "In 1976, Gallagher showed that the Hardy–Littlewood conjectures on prime
k-tuples imply that the\r\ndistribution of primes in log-size intervals is Poissonian.
He did so by computing average values\r\nof the singular series constants over
different sets of a fixed size k contained in an interval [1,h]\r\nas h → ∞, and
then using this average to compute moments of the distribution of primes. In this\r\npaper,
we study averages where k is relatively large with respect to h. We then apply
these averages\r\nto the tail of the distribution. For example, we show, assuming
appropriate Hardy–Littlewood\r\nconjectures and in certain ranges of the parameters,
the number of intervals [n,n + λlogx] with\r\nn ≤ x containing at least k primes
is ≪ x exp(−k/(λe))."
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 with large sets and the tail of the distribution
of primes. The Quarterly Journal of Mathematics. 2023;74(4):1457-1479.
doi:10.1093/qmath/haad030
apa: Kuperberg, V. Z. (2023). Sums of singular series with large sets and the tail
of the distribution of primes. The Quarterly Journal of Mathematics. Oxford
University Press. https://doi.org/10.1093/qmath/haad030
chicago: Kuperberg, Vivian Zieve. “Sums of Singular Series with Large Sets and the
Tail of the Distribution of Primes.” The Quarterly Journal of Mathematics.
Oxford University Press, 2023. https://doi.org/10.1093/qmath/haad030.
ieee: V. Z. Kuperberg, “Sums of singular series with large sets and the tail of the
distribution of primes,” The Quarterly Journal of Mathematics, vol. 74,
no. 4. Oxford University Press, pp. 1457–1479, 2023.
ista: Kuperberg VZ. 2023. Sums of singular series with large sets and the tail of the
distribution of primes. The Quarterly Journal of Mathematics. 74(4), 1457–1479.
mla: Kuperberg, Vivian Zieve. “Sums of Singular Series with Large Sets and the Tail
of the Distribution of Primes.” The Quarterly Journal of Mathematics, vol.
74, no. 4, Oxford University Press, 2023, pp. 1457–79, doi:10.1093/qmath/haad030.
short: V.Z. Kuperberg, The Quarterly Journal of Mathematics 74 (2023) 1457–1479.
date_created: 2026-06-29T12:56:30Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2026-07-14T10:55:52Z
day: '01'
doi: 10.1093/qmath/haad030
extern: '1'
external_id:
arxiv:
- '2210.09775'
intvolume: ' 74'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2210.09775
month: '12'
oa: 1
oa_version: Preprint
page: 1457-1479
publication: The Quarterly Journal of Mathematics
publication_identifier:
eissn:
- 1464-3847
issn:
- 0033-5606
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sums of singular series with large sets and the tail of the distribution of primes
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 74
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '22193'
abstract:
- lang: eng
text: "Gross and Smith have put forward generalizations of Hardy–Littlewood twin
prime\r\nconjectures for algebraic number fields. We estimate the behaviour of
sums of a singular series that arises in these conjectures, up to lower-order
terms. More exactly,\r\nwhere S(η) is the singular series, we find asymptotic
formulas for smoothed sums of\r\nS(η)−1. Based upon Gross and Smith’s conjectures,
we use our result to suggest that\r\nfor large enough ‘short intervals’ in an
algebraic number field K, the variance of counts\r\nof prime elements in a random
short interval deviates from a Cramér model prediction\r\nby a universal factor,
independent of K. The conjecture over number fields generalizes\r\na classical
conjecture of Goldston and Montgomery over the integers. Numerical data\r\nare
provided supporting the conjecture."
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: Brad
full_name: Rodgers, Brad
last_name: Rodgers
- first_name: Edva
full_name: Roditty-Gershon, Edva
last_name: Roditty-Gershon
citation:
ama: Kuperberg VZ, Rodgers B, Roditty-Gershon E. Sums of singular series and primes
in short intervals in algebraic number fields. The Ramanujan Journal. 2022;58(2):291-317.
doi:10.1007/s11139-022-00561-9
apa: Kuperberg, V. Z., Rodgers, B., & Roditty-Gershon, E. (2022). Sums of singular
series and primes in short intervals in algebraic number fields. The Ramanujan
Journal. Springer Nature. https://doi.org/10.1007/s11139-022-00561-9
chicago: Kuperberg, Vivian Zieve, Brad Rodgers, and Edva Roditty-Gershon. “Sums
of Singular Series and Primes in Short Intervals in Algebraic Number Fields.”
The Ramanujan Journal. Springer Nature, 2022. https://doi.org/10.1007/s11139-022-00561-9.
ieee: V. Z. Kuperberg, B. Rodgers, and E. Roditty-Gershon, “Sums of singular series
and primes in short intervals in algebraic number fields,” The Ramanujan Journal,
vol. 58, no. 2. Springer Nature, pp. 291–317, 2022.
ista: Kuperberg VZ, Rodgers B, Roditty-Gershon E. 2022. Sums of singular series
and primes in short intervals in algebraic number fields. The Ramanujan Journal.
58(2), 291–317.
mla: Kuperberg, Vivian Zieve, et al. “Sums of Singular Series and Primes in Short
Intervals in Algebraic Number Fields.” The Ramanujan Journal, vol. 58,
no. 2, Springer Nature, 2022, pp. 291–317, doi:10.1007/s11139-022-00561-9.
short: V.Z. Kuperberg, B. Rodgers, E. Roditty-Gershon, The Ramanujan Journal 58
(2022) 291–317.
date_created: 2026-06-29T12:57:02Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2026-07-14T10:59:34Z
day: '01'
doi: 10.1007/s11139-022-00561-9
extern: '1'
external_id:
arxiv:
- '2001.09513'
intvolume: ' 58'
issue: '2'
keyword:
- Primes
- Short intervals
- Ramanujan sums
- Singular series
- Number fields
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2001.09513
mathsc:
- 11N05
- 11R47
month: '06'
oa: 1
oa_version: Preprint
page: 291-317
publication: The Ramanujan Journal
publication_identifier:
eissn:
- 1572-9303
issn:
- 1382-4090
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Sums of singular series and primes in short intervals in algebraic number fields
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2022'
...
---
OA_place: repository
OA_type: green
_id: '22194'
abstract:
- lang: eng
text: "In [J. P. Keating, B. Rodgers, E. Roditty-Gershon and Z. Rudnick, Sums of
divisor functions in \U0001D53D\U0001D45E[\U0001D461] and matrix integrals, Math.
Z. 288 2018, 1–2, 167–198], the authors established relationships of the mean-square
of sums of the divisor function \U0001D451\U0001D458(\U0001D453) over short intervals
and over arithmetic progressions for the function field \U0001D53D\U0001D45E[\U0001D447]
to certain integrals over the ensemble of unitary matrices. We consider similar
problems leading to distributions over the ensemble of symplectic matrices. We
also consider analogous questions involving convolutions of the von Mangoldt function."
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. Sums of divisor functions and von Mangoldt convolutions
in \U0001D53Dq[T] leading to symplectic distributions. Forum Mathematicum.
2022;34(3):711-747. doi:10.1515/forum-2021-0171"
apa: "Kuperberg, V. Z., & Lalín, M. (2022). Sums of divisor functions and von
Mangoldt convolutions in \U0001D53Dq[T] leading to symplectic distributions. Forum
Mathematicum. De Gruyter. https://doi.org/10.1515/forum-2021-0171"
chicago: "Kuperberg, Vivian Zieve, and Matilde Lalín. “Sums of Divisor Functions
and von Mangoldt Convolutions in \U0001D53Dq[T] Leading to Symplectic Distributions.”
Forum Mathematicum. De Gruyter, 2022. https://doi.org/10.1515/forum-2021-0171."
ieee: "V. Z. Kuperberg and M. Lalín, “Sums of divisor functions and von Mangoldt
convolutions in \U0001D53Dq[T] leading to symplectic distributions,” Forum
Mathematicum, vol. 34, no. 3. De Gruyter, pp. 711–747, 2022."
ista: "Kuperberg VZ, Lalín M. 2022. Sums of divisor functions and von Mangoldt convolutions
in \U0001D53Dq[T] leading to symplectic distributions. Forum Mathematicum. 34(3),
711–747."
mla: "Kuperberg, Vivian Zieve, and Matilde Lalín. “Sums of Divisor Functions and
von Mangoldt Convolutions in \U0001D53Dq[T] Leading to Symplectic Distributions.”
Forum Mathematicum, vol. 34, no. 3, De Gruyter, 2022, pp. 711–47, doi:10.1515/forum-2021-0171."
short: V.Z. Kuperberg, M. Lalín, Forum Mathematicum 34 (2022) 711–747.
date_created: 2026-06-29T12:57:26Z
date_published: 2022-03-26T00:00:00Z
date_updated: 2026-07-14T11:02:45Z
day: '26'
doi: 10.1515/forum-2021-0171
extern: '1'
external_id:
arxiv:
- '2107.01437'
intvolume: ' 34'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2107.01437
month: '03'
oa: 1
oa_version: Preprint
page: 711-747
publication: Forum Mathematicum
publication_identifier:
eissn:
- 1435-5337
issn:
- 0933-7741
publication_status: published
publisher: De Gruyter
quality_controlled: '1'
scopus_import: '1'
status: public
title: "Sums of divisor functions and von Mangoldt convolutions in \U0001D53Dq[T]
leading to symplectic distributions"
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2022'
...
---
OA_place: repository
OA_type: green
_id: '22196'
abstract:
- lang: eng
text: "We explore two questions about pseudo-polynomials, which\r\nare functions
f : N → Z such that k divides f(n + k) −\r\nf(n) for all n, k. First, for certain
arbitrarily sparse sets R, we\r\nconstruct pseudo-polynomials f with p|f(n) for
some n only if\r\np ∈ R. This implies that not all pseudo-polynomials satisfy
an\r\nassumption of a recent paper of Kowalski and Soundararajan.\r\nWe also consider
α-primary pseudo-polynomials, where the\r\npseudo-polynomial condition is only
required for k lying in\r\na set of primes of density α. We show that if an α-primary\r\npseudo-polynomial
is O(e(β−)n), where β = √7\r\n3 − 1\r\n6 ≈ 0.715,\r\nthen it is a polynomial."
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. On pseudo-polynomials divisible only by a sparse set of primes
and α-primary pseudo-polynomials. Journal of Number Theory. 2022;241:531-541.
doi:10.1016/j.jnt.2022.04.006
apa: Kuperberg, V. Z. (2022). On pseudo-polynomials divisible only by a sparse set
of primes and α-primary pseudo-polynomials. Journal of Number Theory. Elsevier.
https://doi.org/10.1016/j.jnt.2022.04.006
chicago: Kuperberg, Vivian Zieve. “On Pseudo-Polynomials Divisible Only by a Sparse
Set of Primes and α-Primary Pseudo-Polynomials.” Journal of Number Theory.
Elsevier, 2022. https://doi.org/10.1016/j.jnt.2022.04.006.
ieee: V. Z. Kuperberg, “On pseudo-polynomials divisible only by a sparse set of
primes and α-primary pseudo-polynomials,” Journal of Number Theory, vol.
241. Elsevier, pp. 531–541, 2022.
ista: Kuperberg VZ. 2022. On pseudo-polynomials divisible only by a sparse set of
primes and α-primary pseudo-polynomials. Journal of Number Theory. 241, 531–541.
mla: Kuperberg, Vivian Zieve. “On Pseudo-Polynomials Divisible Only by a Sparse
Set of Primes and α-Primary Pseudo-Polynomials.” Journal of Number Theory,
vol. 241, Elsevier, 2022, pp. 531–41, doi:10.1016/j.jnt.2022.04.006.
short: V.Z. Kuperberg, Journal of Number Theory 241 (2022) 531–541.
date_created: 2026-06-29T12:58:07Z
date_published: 2022-05-18T00:00:00Z
date_updated: 2026-07-14T11:08:14Z
day: '18'
doi: 10.1016/j.jnt.2022.04.006
extern: '1'
external_id:
arxiv:
- '2006.02527'
intvolume: ' 241'
keyword:
- Pseudo-polynomials
- Chinese remainder theorem
- Ruzsa’s conjecture
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2006.02527
month: '05'
oa: 1
oa_version: Preprint
page: 531-541
publication: Journal of Number Theory
publication_identifier:
issn:
- 0022-314X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: On pseudo-polynomials divisible only by a sparse set of primes and α-primary
pseudo-polynomials
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 241
year: '2022'
...
---
OA_place: repository
OA_type: green
_id: '22205'
abstract:
- lang: eng
text: "A group is sofic when every finite subset can be well approximated in a finite
symmetric group. No example of a non-sofic group is known. Higman's group, which
is a circular amalgamation of four copies of the Baumslag–Solitar group, is a
candidate. Here we contribute to the discussion of the problem of its soficity
in two ways.\r\nWe construct variations on Higman's group replacing the Baumslag–Solitar
group by other groups G. We give an elementary condition on G enjoyed for example
by Z≀Z and the integral Heisenberg group, under which the resulting group is sofic.\r\n\r\nWe
then use soficity to deduce that there exist permutations of Z/nZ that are seemingly
pathological in that they have order dividing four and yet locally they behave
like exponential functions over most of their domains. Our approach is based on
that of Helfgott and Juschenko, who recently showed the soficity of Higman's group
would imply some the existence of some similarly pathological functions. Our results
call into question their suggestion that this might be a step towards proving
the existence of a non-sofic group."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Martin
full_name: Kassabov, Martin
last_name: Kassabov
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
- first_name: Timothy R.
full_name: Riley, Timothy R.
last_name: Riley
citation:
ama: Kassabov M, Kuperberg VZ, Riley TR. Soficity and variations on Higman’s group.
Journal of Combinatorial Algebra. 2019;3(1):41-70. doi:10.4171/jca/26
apa: Kassabov, M., Kuperberg, V. Z., & Riley, T. R. (2019). Soficity and variations
on Higman’s group. Journal of Combinatorial Algebra. European Mathematical
Society. https://doi.org/10.4171/jca/26
chicago: Kassabov, Martin, Vivian Zieve Kuperberg, and Timothy R. Riley. “Soficity
and Variations on Higman’s Group.” Journal of Combinatorial Algebra. European
Mathematical Society, 2019. https://doi.org/10.4171/jca/26.
ieee: M. Kassabov, V. Z. Kuperberg, and T. R. Riley, “Soficity and variations on
Higman’s group,” Journal of Combinatorial Algebra, vol. 3, no. 1. European
Mathematical Society, pp. 41–70, 2019.
ista: Kassabov M, Kuperberg VZ, Riley TR. 2019. Soficity and variations on Higman’s
group. Journal of Combinatorial Algebra. 3(1), 41–70.
mla: Kassabov, Martin, et al. “Soficity and Variations on Higman’s Group.” Journal
of Combinatorial Algebra, vol. 3, no. 1, European Mathematical Society, 2019,
pp. 41–70, doi:10.4171/jca/26.
short: M. Kassabov, V.Z. Kuperberg, T.R. Riley, Journal of Combinatorial Algebra
3 (2019) 41–70.
date_created: 2026-06-29T13:01:27Z
date_published: 2019-02-01T00:00:00Z
date_updated: 2026-07-14T11:54:52Z
day: '01'
doi: 10.4171/jca/26
extern: '1'
external_id:
arxiv:
- '2406.04174'
intvolume: ' 3'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2406.04174
month: '02'
oa: 1
oa_version: Preprint
page: 41-70
publication: Journal of Combinatorial Algebra
publication_identifier:
eissn:
- 2415-6302
publication_status: published
publisher: European Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Soficity and variations on Higman’s group
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2019'
...
---
OA_place: repository
OA_type: green
_id: '22206'
abstract:
- lang: eng
text: 'Cools, Draisma, Payne, and Robeva proved that generic metric graphs that
are "paths of loops" are Brill-Noether general. We show that Brill-Noether generality
does not hold for "trees of loops": the only trees of loops that are Brill-Noether
general are paths of loops. We study various notions of generality and examine
which of these graphs satisfy them.'
article_number: P1.19
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sameer
full_name: Kailasa, Sameer
last_name: Kailasa
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
- first_name: Nicholas
full_name: Wawrykow, Nicholas
last_name: Wawrykow
citation:
ama: Kailasa S, Kuperberg VZ, Wawrykow N. Chip-firing on trees of loops. The
Electronic Journal of Combinatorics. 2018;25(1). doi:10.37236/7244
apa: Kailasa, S., Kuperberg, V. Z., & Wawrykow, N. (2018). Chip-firing on trees
of loops. The Electronic Journal of Combinatorics. The Electronic Journal
of Combinatorics. https://doi.org/10.37236/7244
chicago: Kailasa, Sameer, Vivian Zieve Kuperberg, and Nicholas Wawrykow. “Chip-Firing
on Trees of Loops.” The Electronic Journal of Combinatorics. The Electronic
Journal of Combinatorics, 2018. https://doi.org/10.37236/7244.
ieee: S. Kailasa, V. Z. Kuperberg, and N. Wawrykow, “Chip-firing on trees of loops,”
The Electronic Journal of Combinatorics, vol. 25, no. 1. The Electronic
Journal of Combinatorics, 2018.
ista: Kailasa S, Kuperberg VZ, Wawrykow N. 2018. Chip-firing on trees of loops.
The Electronic Journal of Combinatorics. 25(1), P1.19.
mla: Kailasa, Sameer, et al. “Chip-Firing on Trees of Loops.” The Electronic
Journal of Combinatorics, vol. 25, no. 1, P1.19, The Electronic Journal of
Combinatorics, 2018, doi:10.37236/7244.
short: S. Kailasa, V.Z. Kuperberg, N. Wawrykow, The Electronic Journal of Combinatorics
25 (2018).
date_created: 2026-06-29T13:01:48Z
date_published: 2018-01-25T00:00:00Z
date_updated: 2026-07-14T13:09:11Z
day: '25'
doi: 10.37236/7244
extern: '1'
external_id:
arxiv:
- '1706.04164'
intvolume: ' 25'
issue: '1'
keyword:
- Chip-firing
- Metric graphs
- Brill-Noether generality
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1706.04164
month: '01'
oa: 1
oa_version: Preprint
publication: The Electronic Journal of Combinatorics
publication_identifier:
eissn:
- 1077-8926
publication_status: published
publisher: The Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Chip-firing on trees of loops
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2018'
...
---
OA_place: repository
OA_type: green
_id: '22198'
abstract:
- lang: eng
text: "Packings of equal disks in the plane are known to have density at most\r\nπ/\r\n√\r\n12,
although this density is never achieved in the square torus, which is what we\r\ncall
the plane modulo the square lattice. We find packings of disks in a square torus\r\nthat
we conjecture to be the most dense for certain numbers of packing disks, using\r\ncontinued
fractions to approximate 1/\r\n√\r\n3 and 2 −\r\n√\r\n3. We also define a constant
to\r\nmeasure the efficiency of a packing motived by a related constant due to
Markov for\r\ncontinued fractions. One idea is to use the unique factorization
property of Gaussian\r\nintegers to prove that there is an upper bound for the
Markov constant for grid-like\r\npackings. By way of contrast, we show that an
upper bound by Gruber [In many cases\r\noptimal configurations are almost regular
hexagonal, vol. 65, pp. 121–145, 1999;Geom\r\nDedicata 84(1–3):271–320, 2001]
for the error for the limiting density of a packing\r\nof equal disks in a planar
square, which is on the order of 1/\r\n√\r\nN, is the best possible,\r\nwhereas
for our examples for the square torus, the error for the limiting density is on\r\nthe
order of 1/N, where N is the number of packing disks."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Robert
full_name: Connelly, Robert
last_name: Connelly
- first_name: Matthew
full_name: Funkhouser, Matthew
last_name: Funkhouser
- first_name: Vivian Zieve
full_name: Kuperberg, Vivian Zieve
id: c3bac823-112d-11f0-a3f5-c264f852e697
last_name: Kuperberg
- first_name: Evan
full_name: Solomonides, Evan
last_name: Solomonides
citation:
ama: Connelly R, Funkhouser M, Kuperberg VZ, Solomonides E. Packings of equal disks
in a square torus. Discrete & Computational Geometry. 2017;58(3):614-642.
doi:10.1007/s00454-016-9843-x
apa: Connelly, R., Funkhouser, M., Kuperberg, V. Z., & Solomonides, E. (2017).
Packings of equal disks in a square torus. Discrete & Computational Geometry.
Springer Nature. https://doi.org/10.1007/s00454-016-9843-x
chicago: Connelly, Robert, Matthew Funkhouser, Vivian Zieve Kuperberg, and Evan
Solomonides. “Packings of Equal Disks in a Square Torus.” Discrete & Computational
Geometry. Springer Nature, 2017. https://doi.org/10.1007/s00454-016-9843-x.
ieee: R. Connelly, M. Funkhouser, V. Z. Kuperberg, and E. Solomonides, “Packings
of equal disks in a square torus,” Discrete & Computational Geometry,
vol. 58, no. 3. Springer Nature, pp. 614–642, 2017.
ista: Connelly R, Funkhouser M, Kuperberg VZ, Solomonides E. 2017. Packings of equal
disks in a square torus. Discrete & Computational Geometry. 58(3), 614–642.
mla: Connelly, Robert, et al. “Packings of Equal Disks in a Square Torus.” Discrete
& Computational Geometry, vol. 58, no. 3, Springer Nature, 2017, pp. 614–42,
doi:10.1007/s00454-016-9843-x.
short: R. Connelly, M. Funkhouser, V.Z. Kuperberg, E. Solomonides, Discrete &
Computational Geometry 58 (2017) 614–642.
date_created: 2026-06-29T12:58:50Z
date_published: 2017-01-09T00:00:00Z
date_updated: 2026-07-14T11:14:51Z
day: '09'
doi: 10.1007/s00454-016-9843-x
extern: '1'
external_id:
arxiv:
- '1512.08762'
intvolume: ' 58'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.48550/arXiv.1512.08762
month: '01'
oa_version: Preprint
page: 614-642
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Packings of equal disks in a square torus
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 58
year: '2017'
...
---
OA_place: repository
OA_type: green
_id: '22202'
abstract:
- lang: eng
text: We use modular symmetric designs to study the existence of Hadamard matrices
modulo certain primes. We solve the 7-modular and 11-modular versions of the Hadamard
conjecture for all but a finite number of cases. In doing so, we state a conjectural
sufficient condition for the existence of a p-modular Hadamard matrix for all but
finitely many cases. When 2 is a primitive root of a prime p, we conditionally
solve this conjecture and therefore the p-modular version of the Hadamard conjecture
for all but finitely many cases when p ≡ 3(mod 4), and prove a weaker result for
p ≡ 1 (mod 4). Finally, we look at constraints on the existence of m-modular Hadamard
matrices when the size of the matrix is small compared to m.
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. Hadamard matrices modulo p and small modular Hadamard matrices.
Journal of Combinatorial Designs. 2016;24(9):393-405. doi:10.1002/jcd.21522
apa: Kuperberg, V. Z. (2016). Hadamard matrices modulo p and small modular Hadamard
matrices. Journal of Combinatorial Designs. Wiley. https://doi.org/10.1002/jcd.21522
chicago: Kuperberg, Vivian Zieve. “Hadamard Matrices modulo p and Small Modular
Hadamard Matrices.” Journal of Combinatorial Designs. Wiley, 2016. https://doi.org/10.1002/jcd.21522.
ieee: V. Z. Kuperberg, “Hadamard matrices modulo p and small modular Hadamard matrices,”
Journal of Combinatorial Designs, vol. 24, no. 9. Wiley, pp. 393–405, 2016.
ista: Kuperberg VZ. 2016. Hadamard matrices modulo p and small modular Hadamard
matrices. Journal of Combinatorial Designs. 24(9), 393–405.
mla: Kuperberg, Vivian Zieve. “Hadamard Matrices modulo p and Small Modular Hadamard
Matrices.” Journal of Combinatorial Designs, vol. 24, no. 9, Wiley, 2016,
pp. 393–405, doi:10.1002/jcd.21522.
short: V.Z. Kuperberg, Journal of Combinatorial Designs 24 (2016) 393–405.
date_created: 2026-06-29T13:00:27Z
date_published: 2016-09-01T00:00:00Z
date_updated: 2026-07-14T11:35:58Z
day: '01'
doi: 10.1002/jcd.21522
extern: '1'
external_id:
arxiv:
- '1409.0148'
intvolume: ' 24'
issue: '9'
keyword:
- modular hadamard matrices
- modular symmetric designs
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1409.0148
month: '09'
oa: 1
oa_version: Preprint
page: 393-405
publication: Journal of Combinatorial Designs
publication_identifier:
eissn:
- 1520-6610
issn:
- 1063-8539
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Hadamard matrices modulo p and small modular Hadamard matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2016'
...