Diophantine approximation by algebraic hypersurfaces and varieties
Author:
Wolfgang M. Schmidt
Journal:
Trans. Amer. Math. Soc. 359 (2007), 22212241
MSC (2000):
Primary 11J13, 11J81, 11J82, 11J85
Published electronically:
December 5, 2006
MathSciNet review:
2276618
Fulltext PDF Free Access
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Abstract: Questions on rational approximations to a real number can be generalized in two directions. On the one hand, we may ask about ``approximation'' to a point in by hyperplanes defined over the rationals. That is, we seek hyperplanes with small distance from the given point. On the other hand, following Wirsing, we may ask about approximation to a real number by real algebraic numbers of degree at most . The present paper deals with a common generalization of both directions, namely with approximation to a point in by algebraic hypersurfaces, or more generally algebraic varieties defined over the rationals.
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Additional Information
Wolfgang M. Schmidt
Affiliation:
Department of Mathematics, University of Colorado, Boulder, Colorado 803090395
DOI:
http://dx.doi.org/10.1090/S0002994706040141
PII:
S 00029947(06)040141
Keywords:
Simultaneous approximation,
hypersurfaces,
algebraic independence
Received by editor(s):
October 12, 2004
Received by editor(s) in revised form:
March 10, 2005
Published electronically:
December 5, 2006
Additional Notes:
The author was partially supported by NSF DMS 0074531
Article copyright:
© Copyright 2006
American Mathematical Society
