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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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Upper bounds for the number of integer points on elliptic curves
by
Gary Walsh
University of Ottawa

We apply recent results of Shabnam Akhtari on the number of integer solutions to quartic Thue equations to the problem of determining upper bounds for the number of integer points on cubic and quartic models of elliptic curves. In particular, upper bounds are obtained for the number of integer points on quartic curves of the form x2-dy4=k, with d a nonsquare positive integer, and k any negative integer, and similarly for curves of the form y2=x3+nx, with n negative.

Date received: March 22, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-12.