---
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
has_accepted_license: '1'
intvolume: ' 37'
issue: '3'
language:
- iso: eng
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'
...
---
_id: '12684'
abstract:
- lang: eng
text: Given a place ω of a global function field K over a finite field, with
associated affine function ring Rω and completion Kω , the aim of this paper
is to give an effective joint equidistribution result for renormalized primitive
lattice points (a,b)∈Rω2 in the plane Kω2 , and for renormalized solutions
to the gcd equation ax+by=1 . The main tools are techniques of Goronik and Nevo
for counting lattice points in well-rounded families of subsets. This gives a
sharper analog in positive characteristic of a result of Nevo and the first author
for the equidistribution of the primitive lattice points in \ZZ2 .
acknowledgement: "The authors warmly thank Amos Nevo for having presented the authors
to each other during\r\na beautiful conference in Goa in February 2016, where the
idea of this paper was born. The\r\nfirst author thanks the IHES for two post-doctoral
years when most of this paper was discussed,\r\nand the Topology team in Orsay for
financial support at the final stage. The first author was\r\nsupported by the EPRSC
EP/P026710/1 grant. Finally, we warmly thank the referee for many\r\nvery helpful
comments that have improved the readability of this paper."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tal
full_name: Horesh, Tal
id: C8B7BF48-8D81-11E9-BCA9-F536E6697425
last_name: Horesh
- first_name: Frédéric
full_name: Paulin, Frédéric
last_name: Paulin
citation:
ama: Horesh T, Paulin F. Effective equidistribution of lattice points in positive
characteristic. Journal de Theorie des Nombres de Bordeaux. 2022;34(3):679-703.
doi:10.5802/JTNB.1222
apa: Horesh, T., & Paulin, F. (2022). Effective equidistribution of lattice
points in positive characteristic. Journal de Theorie Des Nombres de Bordeaux.
Université de Bordeaux. https://doi.org/10.5802/JTNB.1222
chicago: Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice
Points in Positive Characteristic.” Journal de Theorie Des Nombres de Bordeaux.
Université de Bordeaux, 2022. https://doi.org/10.5802/JTNB.1222.
ieee: T. Horesh and F. Paulin, “Effective equidistribution of lattice points in
positive characteristic,” Journal de Theorie des Nombres de Bordeaux, vol.
34, no. 3. Université de Bordeaux, pp. 679–703, 2022.
ista: Horesh T, Paulin F. 2022. Effective equidistribution of lattice points in
positive characteristic. Journal de Theorie des Nombres de Bordeaux. 34(3), 679–703.
mla: Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points
in Positive Characteristic.” Journal de Theorie Des Nombres de Bordeaux,
vol. 34, no. 3, Université de Bordeaux, 2022, pp. 679–703, doi:10.5802/JTNB.1222.
short: T. Horesh, F. Paulin, Journal de Theorie Des Nombres de Bordeaux 34 (2022)
679–703.
corr_author: '1'
das_tickbox: '0'
date_created: 2023-02-26T23:01:02Z
date_published: 2022-01-27T00:00:00Z
date_updated: 2026-07-29T10:46:58Z
day: '27'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.5802/JTNB.1222
external_id:
arxiv:
- '2001.01534'
isi:
- '000926504300003'
file:
- access_level: open_access
checksum: 08f28fded270251f568f610cf5166d69
content_type: application/pdf
creator: dernst
date_created: 2023-02-27T09:10:13Z
date_updated: 2023-02-27T09:10:13Z
file_id: '12689'
file_name: 2023_JourTheorieNombreBordeaux_Horesh.pdf
file_size: 870468
relation: main_file
success: 1
file_date_updated: 2023-02-27T09:10:13Z
has_accepted_license: '1'
intvolume: ' 34'
isi: 1
issue: '3'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 679-703
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: Effective equidistribution of lattice points in positive characteristic
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: 34
year: '2022'
...
---
_id: '2904'
abstract:
- lang: eng
text: Generalized van der Corput sequences are onedimensional, infinite sequences
in the unit interval. They are generated from permutations in integer base b and
are the building blocks of the multi-dimensional Halton sequences. Motivated by
recent progress of Atanassov on the uniform distribution behavior of Halton sequences,
we study, among others, permutations of the form P(i) = ai (mod b) for coprime
integers a and b. We show that multipliers a that either divide b - 1 or b + 1
generate van der Corput sequences with weak distribution properties. We give explicit
lower bounds for the asymptotic distribution behavior of these sequences and relate
them to sequences generated from the identity permutation in smaller bases, which
are, due to Faure, the weakest distributed generalized van der Corput sequences.
- lang: fre
text: Les suites de Van der Corput généralisées sont dessuites unidimensionnelles
et infinies dans l’intervalle de l’unité.Elles sont générées par permutations
des entiers de la basebetsont les éléments constitutifs des suites multi-dimensionnelles
deHalton. Suites aux progrès récents d’Atanassov concernant le com-portement de
distribution uniforme des suites de Halton nous nousintéressons aux permutations
de la formuleP(i) =ai(modb)pour les entiers premiers entre euxaetb. Dans cet
article nousidentifions des multiplicateursagénérant des suites de Van derCorput
ayant une mauvaise distribution. Nous donnons les bornesinférieures explicites
pour cette distribution asymptotique asso-ciée à ces suites et relions ces dernières
aux suites générées parpermutation d’identité, qui sont, selon Faure, les moins
bien dis-tribuées des suites généralisées de Van der Corput dans une basedonnée.
article_processing_charge: No
article_type: original
author:
- first_name: Florian
full_name: Pausinger, Florian
id: 2A77D7A2-F248-11E8-B48F-1D18A9856A87
last_name: Pausinger
orcid: 0000-0002-8379-3768
citation:
ama: Pausinger F. Weak multipliers for generalized van der Corput sequences. Journal
de Theorie des Nombres des Bordeaux. 2012;24(3):729-749. doi:10.5802/jtnb.819
apa: Pausinger, F. (2012). Weak multipliers for generalized van der Corput sequences.
Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux. https://doi.org/10.5802/jtnb.819
chicago: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.”
Journal de Theorie Des Nombres Des Bordeaux. Université de Bordeaux, 2012.
https://doi.org/10.5802/jtnb.819.
ieee: F. Pausinger, “Weak multipliers for generalized van der Corput sequences,”
Journal de Theorie des Nombres des Bordeaux, vol. 24, no. 3. Université
de Bordeaux, pp. 729–749, 2012.
ista: Pausinger F. 2012. Weak multipliers for generalized van der Corput sequences.
Journal de Theorie des Nombres des Bordeaux. 24(3), 729–749.
mla: Pausinger, Florian. “Weak Multipliers for Generalized van Der Corput Sequences.”
Journal de Theorie Des Nombres Des Bordeaux, vol. 24, no. 3, Université
de Bordeaux, 2012, pp. 729–49, doi:10.5802/jtnb.819.
short: F. Pausinger, Journal de Theorie Des Nombres Des Bordeaux 24 (2012) 729–749.
date_created: 2018-12-11T12:00:15Z
date_published: 2012-01-01T00:00:00Z
date_updated: 2025-09-30T08:18:15Z
day: '01'
ddc:
- '510'
department:
- _id: HeEd
doi: 10.5802/jtnb.819
external_id:
isi:
- '000315243100011'
file:
- access_level: open_access
checksum: 6954bfe9d7f4119fbdda7a11cf0f5c67
content_type: application/pdf
creator: dernst
date_created: 2020-05-11T12:40:39Z
date_updated: 2020-07-14T12:45:52Z
file_id: '7819'
file_name: JTNB_2012__24_3_729_0.pdf
file_size: 819275
relation: main_file
file_date_updated: 2020-07-14T12:45:52Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
issue: '3'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 729 - 749
publication: Journal de Theorie des Nombres des Bordeaux
publication_identifier:
eissn:
- 2118-8572
issn:
- 1246-7405
publication_status: published
publisher: Université de Bordeaux
publist_id: '3843'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Weak multipliers for generalized van der Corput sequences
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 24
year: '2012'
...