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.References
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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
- 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
- © Copyright 1996 American Mathematical Society
- 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