Computing integral points on hyperelliptic curves using quadratic chabauty

Jennifer S. Balakrishnan; Amnon Besser; J. Steffen Müller

doi:10.1090/mcom/3130

Computing integral points on hyperelliptic curves using quadratic chabauty

Jennifer S. Balakrishnan, Amnon Besser, J. Steffen Müller

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the p-adic approximation techniques introduced in previous work with the Mordell-Weil sieve.

Original language	English
Pages (from-to)	1403-1434
Number of pages	32
Journal	Mathematics of Computation
Volume	86
Issue number	305
DOIs	https://doi.org/10.1090/mcom/3130
State	Published - 1 Jan 2017

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics
Applied Mathematics

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title = "Computing integral points on hyperelliptic curves using quadratic chabauty",

abstract = "We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the p-adic approximation techniques introduced in previous work with the Mordell-Weil sieve.",

author = "Balakrishnan, {Jennifer S.} and Amnon Besser and {Steffen M{\"u}ller}, J.",

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AU - Balakrishnan, Jennifer S.

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AU - Steffen Müller, J.

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N2 - We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the p-adic approximation techniques introduced in previous work with the Mordell-Weil sieve.

AB - We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the p-adic approximation techniques introduced in previous work with the Mordell-Weil sieve.

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DO - 10.1090/mcom/3130

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EP - 1434

JO - Mathematics of Computation

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ER -

Computing integral points on hyperelliptic curves using quadratic chabauty

Abstract

ASJC Scopus subject areas

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