Heights of algebraic points lying on curves or hypersurfaces

Schmidt, Wolfgang

doi:10.1090/S0002-9939-96-03519-8

Heights of algebraic points lying on curves or hypersurfaces
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by Wolfgang M. Schmidt PDF

Proc. Amer. Math. Soc. 124 (1996), 3003-3013 Request permission

Abstract:

Our first aim will be to give an explicit version of a generalization of the results of Zhang and Zagier on algebraic points $(x,y)$ with $x+y+ 1 = 0$. Secondly, we will show that distinct algebraic points lying on a given curve of certain type can be distinguished in terms of some height functions. Thirdly, we will derive a bound for the number of points on such a curve whose heights are under a given bound and whose coordinates lie in a multiplicative group of given rank.

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