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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On simultaneous uniform approximation to a $p$-adic number and its square
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by Yann Bugeaud PDF
Proc. Amer. Math. Soc. 138 (2010), 3821-3826 Request permission

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
  • Received by editor(s): January 29, 2010
  • Published electronically: May 21, 2010
  • Communicated by: Ken Ono
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2679605