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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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On Kummer’s twenty-four solutions of the hypergeometric differential equation
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by B. Dwork PDF
Trans. Amer. Math. Soc. 285 (1984), 497-521 Request permission

Abstract:

The $p$-adic analyticity of the Boyarsky matrix associated with the hypergeometric function $F(a,b;c;x)$ has been investigated in an earlier article. The transformation of this matrix under translation of $(a, b, c)$ by ${{\bf {Z}}^3}$ was determined at that time. This article gives the transformation of this matrix under the extended Kummer group. The $p$-adic implications of quadratic and higher-degree transformations remain open.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 285 (1984), 497-521
  • MSC: Primary 12H25; Secondary 14G20, 33A30, 34A30
  • DOI: https://doi.org/10.1090/S0002-9947-1984-0752488-X
  • MathSciNet review: 752488