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Mathematics of Computation

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Computing integral points on hyperelliptic curves using quadratic Chabauty


Authors: Jennifer S. Balakrishnan, Amnon Besser and J. Steffen Müller
Journal: Math. Comp. 86 (2017), 1403-1434
MSC (2010): Primary 11G30; Secondary 11S80, 11Y50, 14G40
DOI: https://doi.org/10.1090/mcom/3130
Published electronically: October 12, 2016
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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.


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Additional Information

Jennifer S. Balakrishnan
Affiliation: Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom

Amnon Besser
Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Be’er-Sheva 84105, Israel

J. Steffen Müller
Affiliation: Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany

DOI: https://doi.org/10.1090/mcom/3130
Received by editor(s): May 2, 2015
Received by editor(s) in revised form: November 3, 2015
Published electronically: October 12, 2016
Article copyright: © Copyright 2016 American Mathematical Society