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S-integral points on hyperelliptic curves
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Gallegos-Ruiz, Homero R. (2011) S-integral points on hyperelliptic curves. International Journal of Number Theory, Volume 7 (Number 3). p. 803. doi:10.1142/S1793042111004435 ISSN 1793-0421.
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Official URL: http://dx.doi.org/10.1142/S1793042111004435
Abstract
Let C : Y(2) = a(n)X(n) + ... + a(0) be a hyperelliptic curve with the a(i) rational integers, n >= 5, and the polynomial on the right irreducible. Let J be its Jacobian. Let S be a finite set of rational primes. We give a completely explicit upper bound for the size of the S-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 use a refinement of the Mordell-Weil sieve which, combined with the upper bound, is capable of determining all the S-integral points. The method is illustrated by determining the S-integral points on the genus 2 hyperelliptic model Y(2) - Y = X(5) - X for the set S of the first 22 primes.
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, Integrals, Hyperelliptic | ||||
Journal or Publication Title: | International Journal of Number Theory | ||||
Publisher: | World Scientific Publishing Co. Pte. Ltd. | ||||
ISSN: | 1793-0421 | ||||
Official Date: | 2011 | ||||
Dates: |
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Volume: | Volume 7 | ||||
Number: | Number 3 | ||||
Page Range: | p. 803 | ||||
DOI: | 10.1142/S1793042111004435 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Funder: | Consejo Nacional de Ciencia y Tecnología (Mexico) [Mexican Council for Science and Technology] (CONACYT) | ||||
Grant number: | 160194 (CONACYT) |
Data sourced from Thomson Reuters' Web of Knowledge
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