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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computing integral points on hyperelliptic curves using quadratic Chabauty
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by Jennifer S. Balakrishnan, Amnon Besser and J. Steffen Müller PDF
Math. Comp. 86 (2017), 1403-1434 Request permission

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
  • MR Author ID: 910890
  • Amnon Besser
  • Affiliation: Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Be’er-Sheva 84105, Israel
  • MR Author ID: 364540
  • J. Steffen Müller
  • Affiliation: Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany
  • MR Author ID: 895560
  • Received by editor(s): May 2, 2015
  • Received by editor(s) in revised form: November 3, 2015
  • Published electronically: October 12, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 1403-1434
  • MSC (2010): Primary 11G30; Secondary 11S80, 11Y50, 14G40
  • DOI: https://doi.org/10.1090/mcom/3130
  • MathSciNet review: 3614022