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On simultaneous uniform approximation to a $ p$-adic number and its square


Author: Yann Bugeaud
Journal: Proc. Amer. Math. Soc. 138 (2010), 3821-3826
MSC (2010): Primary 11J13, 11J61
DOI: https://doi.org/10.1090/S0002-9939-2010-10491-4
Published electronically: May 21, 2010
MathSciNet review: 2679605
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Abstract: Let $ p$ be a prime number. We show that a result of Teulié is nearly best possible by constructing a $ p$-adic number $ \xi$ such that $ \xi$ and $ \xi^2$ are uniformly simultaneously very well approximable by rational numbers with the same denominator. The same conclusion was previously reached by Zelo in his PhD thesis, but our approach using $ p$-adic continued fractions is more direct and simpler.


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Additional Information

Yann Bugeaud
Affiliation: Département de Mathématiques, Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg, France
Email: bugeaud@math.unistra.fr

DOI: https://doi.org/10.1090/S0002-9939-2010-10491-4
Received by editor(s): January 29, 2010
Published electronically: May 21, 2010
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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