Vol. 15, No. 3, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Computing integral points on $X_{\mathrm{ns}}^+(p)$

Aurélien Bajolet, Yuri Bilu and Benjamin Matschke

Vol. 15 (2021), No. 3, 569–608
Abstract

We develop a general method for computing integral points on modular curves, based on Baker’s inequality. As an illustration, we show that for 11 p < 101, the only integral points on the curve Xns+(p) are the CM points.

To the memory of Alan Baker

Keywords
modular curves, normalizers, nonsplit Cartan subgroups, integral points, Serre's uniformity problem, economical modular units, Baker–Davenport method, lattice point enumeration
Mathematical Subject Classification 2010
Primary: 11-04
Secondary: 11G16, 11Y40, 14G05
Milestones
Received: 23 October 2018
Revised: 27 July 2020
Accepted: 10 October 2020
Published: 20 May 2021
Authors
Aurélien Bajolet
Lycée Jean Dautet
La Rochelle
France
Yuri Bilu
Institut de Mathématiques de Bordeaux
Université de Bordeaux & CNRS
Talence
France
Benjamin Matschke
Department of Mathematics and Statistics
Boston University
Boston, MA
United States