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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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The irrationality of $\log (1+1/q) \log (1-1/q)$
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by Masayoshi Hata PDF
Trans. Amer. Math. Soc. 350 (1998), 2311-2327 Request permission

Abstract:

We shall show that the numbers $1, \log (1+ 1/q), \log (1-1/q)$ and $\log (1+1/q)\log (1-1/q)$ are linearly independent over $\mathbf {Q}$ for any natural number $q \ge 54$. The key is to construct explicit Padé-type approximations using Legendre-type polynomials.
References
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Additional Information
  • Masayoshi Hata
  • Affiliation: Division of Mathematics, Faculty of Integrated Human Studies, Kyoto University, Kyoto 606-01, Japan
  • Email: hata@i.h.kyoto-u.ac.jp
  • Received by editor(s): April 14, 1995
  • Received by editor(s) in revised form: March 21, 1996
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2311-2327
  • MSC (1991): Primary 11J72; Secondary 11J82
  • DOI: https://doi.org/10.1090/S0002-9947-98-01764-4
  • MathSciNet review: 1390038