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Sintegral points on hyperelliptic curves
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GallegosRuiz, Homero R.. (2011) Sintegral points on hyperelliptic curves. International Journal of Number Theory, Volume 7 (Number 3). p. 803. ISSN 17930421
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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 Sintegral points on the model C, provided we know at least one rational point on C and a MordellWeil basis for J(Q). We use a refinement of the MordellWeil sieve which, combined with the upper bound, is capable of determining all the Sintegral points. The method is illustrated by determining the Sintegral 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 > 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:  17930421  
Official Date:  2011  
Dates: 


Volume:  Volume 7  
Number:  Number 3  
Page Range:  p. 803  
Identification Number:  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)  
References:  [1] A. Baker, Bounds for the solutions of the hyperelliptic equation, Math. Proc. Cambridge 

URI:  http://wrap.warwick.ac.uk/id/eprint/41337 
Data sourced from Thomson Reuters' Web of Knowledge
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