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Thue's equation over function fields

Published online by Cambridge University Press:  09 April 2009

Wolfgang M. Schmidt
Wolfgang M. Schmidt
Affiliation:
University of ColoradoBoulder, Colorado 80309, USA
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Abstract

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Suppose we are given a “Thue equation” f(x, y) = 1, where f is a binary form with coefficients in a function field K of characteristic zero. A typical result is that if f is of degree at least 5 and has no multiple factors, then every solution x = (x, y) of the equation with components in K has H(x)≤90H(f) + 250g. Here g is the genus of K and H(x), H(f) are suitably defined heights. No assumption is made that x be “integral” in some sense. As an application, bounds are derived for “integral” solutions of hyperelliptic equations over K.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 4 , June 1978 , pp. 385 - 422
Copyright
Copyright © Australian Mathematical Society 1978

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