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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Simultaneous rational approximation to binomial functions
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by Michael A. Bennett PDF
Trans. Amer. Math. Soc. 348 (1996), 1717-1738 Request permission

Abstract:

We apply Padé approximation techniques to deduce lower bounds for simultaneous rational approximation to one or more algebraic numbers. In particular, we strengthen work of Osgood, Fel′dman and Rickert, proving, for example, that \[ \max \left \{ \left | \sqrt {2} - p_{1}/q \right | , \left | \sqrt {3} - p_{2}/q \right | \right \} > q^{-1.79155} \] for $q > q_{0}$ (where the latter is an effective constant). Some of the Diophantine consequences of such bounds will be discussed, specifically in the direction of solving simultaneous Pell’s equations and norm form equations.
References
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Additional Information
  • Michael A. Bennett
  • Affiliation: Department of Pure Mathematics, The University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
  • Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • MR Author ID: 339361
  • Email: mabennet@math.lsa.umich.edu
  • Received by editor(s): June 30, 1994
  • Received by editor(s) in revised form: January 31, 1995
  • Additional Notes: Research supported by an NSERC Postdoctoral Fellowship
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 1717-1738
  • MSC (1991): Primary 11J68, 11J82; Secondary 11D57
  • DOI: https://doi.org/10.1090/S0002-9947-96-01480-8
  • MathSciNet review: 1321566