Rational and Integral Points on Quadratic Twists of a Given Hyperelliptic Curve

Andrew Granville

Type: Article

Publication Date: 2007-06-21

Citations: 32

DOI: https://doi.org/10.1093/imrn/rnm027

Abstract

We show that the abc-conjecture implies that few quadratic twists of a given hyperelliptic curve have any non-trivial rational or integral points; and indicate how these considerations dovetail with other predictions.

Locations

International Mathematics Research Notices - View
CiteSeer X (The Pennsylvania State University) - View - PDF

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