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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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 |
|---|---|
| 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: | Date Event 2011 Published |
| 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) |
| URI: | https://wrap.warwick.ac.uk/41337/ |
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