Computing integral points on Xns+(p)

Aurélien Bajolet; Yuri Bilu; Benjamin Matschke

doi:10.2140/ant.2021.15.569

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 $11 \le p < 101$ , the only integral points on the curve $X_{ns}^ + \left( p \right)$ are the CM points.

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Aurélien Bajolet. Yuri Bilu. Benjamin Matschke. "Computing integral points on $X_{{\rm{ns}}}^ + (p)$ ." Algebra Number Theory 15 (3) 569 - 608, 2021. https://doi.org/10.2140/ant.2021.15.569

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Received: 23 October 2018; Revised: 27 July 2020; Accepted: 10 October 2020; Published: 2021

First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/ant.2021.15.569

Subjects:

Primary: 11-04

Secondary: 11G16 , 11Y40 , 14G05

Keywords: Baker–Davenport method , economical modular units , Integral points , lattice point enumeration , modular curves , nonsplit Cartan subgroups , normalizers , Serre's uniformity problem

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