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Integral points on hyperelliptic curves

Title data

Bugeaud, Yann ; Mignotte, Maurice ; Siksek, Samir ; Stoll, Michael ; Tengely, Szabolcs:
Integral points on hyperelliptic curves.
In: Algebra & Number Theory. Vol. 2 (2008) Issue 8 . - pp. 859-885.
ISSN 1937-0652
DOI: https://doi.org/10.2140/ant.2008.2.859

Abstract in another language

Let C: Y2=a_n X^n+...+a_0 be a hyperelliptic curve with the a_i 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 binom(Y,2)=binom(X,5).

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: curve; integral point; Jacobian; height; Mordell-Weil group; Baker’s bound; Mordell-Weil sieve
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 26 Jan 2015 09:41
Last Modified: 26 Jan 2015 09:41
URI: https://eref.uni-bayreuth.de/id/eprint/5998