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On Kummer's twenty-four solutions of the hypergeometric differential equation

Author: B. Dwork
Journal: Trans. Amer. Math. Soc. 285 (1984), 497-521
MSC: Primary 12H25; Secondary 14G20, 33A30, 34A30
MathSciNet review: 752488
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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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Article copyright: © Copyright 1984 American Mathematical Society