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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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Rational approximations to the dilogarithm
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by Masayoshi Hata PDF
Trans. Amer. Math. Soc. 336 (1993), 363-387 Request permission

Abstract:

The irrationality proof of the values of the dilogarithmic function ${L_2}(z)$ at rational points $z = 1/k$ for every integer $k \in ( - \infty , - 5] \cup [7,\infty )$ is given. To show this we develop the method of Padé-type approximations using Legendre-type polynomials, which also derives good irrationality measures of ${L_2}(1/k)$. Moreover, the linear independence over ${\mathbf {Q}}$ of the numbers $1$, $\log (1 - 1/k)$, and ${L_2}(1/k)$ is also obtained for each integer $k \in ( - \infty , - 5] \cup [7,\infty )$ .
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 336 (1993), 363-387
  • MSC: Primary 11J82; Secondary 11J72
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1147401-5
  • MathSciNet review: 1147401