---
OA_place: repository
OA_type: green
_id: '19483'
abstract:
- lang: eng
  text: We prove matching upper and lower bounds for the average of the6-torsionof
    class groups of quadratic fields. Furthermore, we count the number of integer
    solutions on an affine quartic threefold.
article_number: '18'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yik Tung
  full_name: Chan, Yik Tung
  id: c4c0afc8-9262-11ed-9231-d8b0bc743af1
  last_name: Chan
  orcid: 0000-0001-8467-4106
- first_name: Peter
  full_name: Koymans, Peter
  last_name: Koymans
- first_name: Carlo
  full_name: Pagano, Carlo
  last_name: Pagano
- first_name: Efthymios
  full_name: Sofos, Efthymios
  last_name: Sofos
citation:
  ama: Chan S, Koymans P, Pagano C, Sofos E. 6-torision and integral points on quartic
    threefolds. <i>Annali della Scuola Normale Superiore di Pisa, Classe di Scienze</i>.
    2025. doi:<a href="https://doi.org/10.2422/2036-2145.202412_006">10.2422/2036-2145.202412_006</a>
  apa: Chan, S., Koymans, P., Pagano, C., &#38; Sofos, E. (2025). 6-torision and integral
    points on quartic threefolds. <i>Annali Della Scuola Normale Superiore Di Pisa,
    Classe Di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale. <a href="https://doi.org/10.2422/2036-2145.202412_006">https://doi.org/10.2422/2036-2145.202412_006</a>
  chicago: Chan, Stephanie, Peter Koymans, Carlo Pagano, and Efthymios Sofos. “6-Torision
    and Integral Points on Quartic Threefolds.” <i>Annali Della Scuola Normale Superiore
    Di Pisa, Classe Di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale,
    2025. <a href="https://doi.org/10.2422/2036-2145.202412_006">https://doi.org/10.2422/2036-2145.202412_006</a>.
  ieee: S. Chan, P. Koymans, C. Pagano, and E. Sofos, “6-torision and integral points
    on quartic threefolds,” <i>Annali della Scuola Normale Superiore di Pisa, Classe
    di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale, 2025.
  ista: Chan S, Koymans P, Pagano C, Sofos E. 2025. 6-torision and integral points
    on quartic threefolds. Annali della Scuola Normale Superiore di Pisa, Classe di
    Scienze., 18.
  mla: Chan, Stephanie, et al. “6-Torision and Integral Points on Quartic Threefolds.”
    <i>Annali Della Scuola Normale Superiore Di Pisa, Classe Di Scienze</i>, 18, Scuola
    Normale Superiore - Edizioni della Normale, 2025, doi:<a href="https://doi.org/10.2422/2036-2145.202412_006">10.2422/2036-2145.202412_006</a>.
  short: S. Chan, P. Koymans, C. Pagano, E. Sofos, Annali Della Scuola Normale Superiore
    Di Pisa, Classe Di Scienze (2025).
corr_author: '1'
das_tickbox: '0'
date_created: 2025-04-05T10:49:27Z
date_published: 2025-03-07T00:00:00Z
date_updated: 2026-07-16T09:35:52Z
day: '07'
department:
- _id: TiBr
doi: 10.2422/2036-2145.202412_006
external_id:
  arxiv:
  - '2403.13359'
fulldoi: https://doi.org/10.2422/2036-2145.202412_006
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2403.13359'
month: '03'
oa: 1
oa_version: Preprint
publication: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
publication_identifier:
  eissn:
  - 2036-2145
  issn:
  - 0391-173X
publication_status: epub_ahead
publisher: Scuola Normale Superiore - Edizioni della Normale
researchdata_availability: no
status: public
supplementarymaterial: no
title: 6-torision and integral points on quartic threefolds
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2025'
...
---
_id: '12916'
abstract:
- lang: eng
  text: "We apply a variant of the square-sieve to produce an upper bound for the
    number of rational points of bounded height on a family of surfaces that admit
    a fibration over P1 whose general fibre is a hyperelliptic curve. The implied
    constant does not depend on the coefficients of the polynomial defining the surface.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dante
  full_name: Bonolis, Dante
  id: 6A459894-5FDD-11E9-AF35-BB24E6697425
  last_name: Bonolis
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
citation:
  ama: Bonolis D, Browning TD. Uniform bounds for rational points on hyperelliptic
    fibrations. <i>Annali della Scuola Normale Superiore di Pisa, Classe di Scienze</i>.
    2023;24(1):173-204. doi:<a href="https://doi.org/10.2422/2036-2145.202010_018">10.2422/2036-2145.202010_018</a>
  apa: Bonolis, D., &#38; Browning, T. D. (2023). Uniform bounds for rational points
    on hyperelliptic fibrations. <i>Annali Della Scuola Normale Superiore Di Pisa,
    Classe Di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale. <a href="https://doi.org/10.2422/2036-2145.202010_018">https://doi.org/10.2422/2036-2145.202010_018</a>
  chicago: Bonolis, Dante, and Timothy D Browning. “Uniform Bounds for Rational Points
    on Hyperelliptic Fibrations.” <i>Annali Della Scuola Normale Superiore Di Pisa,
    Classe Di Scienze</i>. Scuola Normale Superiore - Edizioni della Normale, 2023.
    <a href="https://doi.org/10.2422/2036-2145.202010_018">https://doi.org/10.2422/2036-2145.202010_018</a>.
  ieee: D. Bonolis and T. D. Browning, “Uniform bounds for rational points on hyperelliptic
    fibrations,” <i>Annali della Scuola Normale Superiore di Pisa, Classe di Scienze</i>,
    vol. 24, no. 1. Scuola Normale Superiore - Edizioni della Normale, pp. 173–204,
    2023.
  ista: Bonolis D, Browning TD. 2023. Uniform bounds for rational points on hyperelliptic
    fibrations. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.
    24(1), 173–204.
  mla: Bonolis, Dante, and Timothy D. Browning. “Uniform Bounds for Rational Points
    on Hyperelliptic Fibrations.” <i>Annali Della Scuola Normale Superiore Di Pisa,
    Classe Di Scienze</i>, vol. 24, no. 1, Scuola Normale Superiore - Edizioni della
    Normale, 2023, pp. 173–204, doi:<a href="https://doi.org/10.2422/2036-2145.202010_018">10.2422/2036-2145.202010_018</a>.
  short: D. Bonolis, T.D. Browning, Annali Della Scuola Normale Superiore Di Pisa,
    Classe Di Scienze 24 (2023) 173–204.
corr_author: '1'
das_tickbox: '0'
date_created: 2023-05-07T22:01:04Z
date_published: 2023-02-16T00:00:00Z
date_updated: 2026-07-29T10:10:35Z
day: '16'
department:
- _id: TiBr
doi: 10.2422/2036-2145.202010_018
external_id:
  arxiv:
  - '2007.14182'
fulldoi: https://doi.org/10.2422/2036-2145.202010_018
intvolume: '        24'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2007.14182
month: '02'
oa: 1
oa_version: Preprint
page: 173-204
publication: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
publication_identifier:
  eissn:
  - 2036-2145
  issn:
  - 0391-173X
publication_status: published
publisher: Scuola Normale Superiore - Edizioni della Normale
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Uniform bounds for rational points on hyperelliptic fibrations
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 24
year: '2023'
...