Heights of algebraic points lying on curves or hypersurfaces
Author:
Wolfgang M. Schmidt
Journal:
Proc. Amer. Math. Soc. 124 (1996), 30033013
MSC (1991):
Primary 11G30
MathSciNet review:
1343724
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Abstract: Our first aim will be to give an explicit version of a generalization of the results of Zhang and Zagier on algebraic points with . 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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 H. P. Schlickewei, Equations , Annals of Math., (to appear).
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 H. P. Schlickewei and W. M. Schmidt, Linear equations in variables which lie in a multiplicative group, In preparation.
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 H. P. Schlickewei and E. Wirsing, Lower bounds for the heights of solutions of linear equations, Invent. Math, (to appear).
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 S. Zhang, Positive line bundles on arithmetic surfaces, Ann. of Math. 136 (1992), 569587. MR 93j:14024
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Additional Information
Wolfgang M. Schmidt
Affiliation:
Department of Mathematics, University of Colorado, Boulder, Colorado 803090395
Email:
Schmidt@Euclid.colorado.edu
DOI:
http://dx.doi.org/10.1090/S0002993996035198
PII:
S 00029939(96)035198
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
