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Computing integral
points on $X_{\mathrm{ns}}^+(p)$
Aurélien Bajolet, Yuri Bilu and Benjamin Matschke |
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Vol. 15 (2021), No. 3, 569–608
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Abstract |
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We develop a general method for computing integral points on modular curves, based on Baker’s inequality. As an illustration, we show that for , the only integral points on the curve are the CM points. |
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To the memory of Alan Baker |
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Keywords
modular curves, normalizers, nonsplit Cartan subgroups,
integral points, Serre's uniformity problem, economical
modular units, Baker–Davenport method, lattice point
enumeration
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Mathematical Subject Classification 2010
Primary: 11-04
Secondary: 11G16, 11Y40, 14G05
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Milestones
Received: 23 October 2018
Revised: 27 July 2020
Accepted: 10 October 2020
Published: 20 May 2021
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Authors |
| Aurélien Bajolet | |
| Lycée Jean Dautet La Rochelle France |
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| Yuri Bilu | |
| Institut de Mathématiques de
Bordeaux Université de Bordeaux & CNRS Talence France |
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| Benjamin Matschke | |
| Department of Mathematics and
Statistics Boston University Boston, MA United States |
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