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Integral points on hyperelliptic curves
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Bugeaud, Yann, Mignotte, Maurice, Siksek, Samir, Stoll, M. and Tengely, Szabolcs (2008) Integral points on hyperelliptic curves. Algebra & Number Theory, Vol.2 (No.8). pp. 859-885. doi:DOI: 10.2140/ant.2008.2.859 ISSN 1937-0652.
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Official URL: http://dx.doi.org/10.2140/ant.2008.2.859
Abstract
Let C : Y-2 = a(n)X(n)+...+a(0) be a hyperelliptic curve with the ai rational integers, n >= 5, and the polynomial on the right- hand side irreducible. Let J be its Jacobian. We give a completely explicit upper bound for the integral points on the model C, provided we know at least one rational point on C and a Mordell Weil basis for J (Q). We also explain a powerful refinement of the Mordell - Weil sieve which, combined with the upper bound, is capable of determining all the integral points. Our method is illustrated by determining the integral points on the genus 2 hyperelliptic models Y-2 - Y = X-5 - X and (Y 2) = (X 5).
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Curves, Elliptic, Jacobians | ||||
Journal or Publication Title: | Algebra & Number Theory | ||||
Publisher: | Mathematical Sciences Publishers | ||||
ISSN: | 1937-0652 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.2 | ||||
Number: | No.8 | ||||
Number of Pages: | 27 | ||||
Page Range: | pp. 859-885 | ||||
DOI: | DOI: 10.2140/ant.2008.2.859 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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