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Heights of algebraic points lying
on curves or hypersurfaces


Author: Wolfgang M. Schmidt
Journal: Proc. Amer. Math. Soc. 124 (1996), 3003-3013
MSC (1991): Primary 11G30
DOI: https://doi.org/10.1090/S0002-9939-96-03519-8
MathSciNet review: 1343724
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Wolfgang M. Schmidt
Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80309-0395
Email: Schmidt@Euclid.colorado.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03519-8
Received by editor(s): March 27, 1995
Additional Notes: The author was supported in part by NSF grant DMS–9401426.
Communicated by: William W. Adams
Article copyright: © Copyright 1996 American Mathematical Society

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