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Zbl 0644.10019
Stiller, P.F.
Classical automorphic forms and hypergeometric functions. (English)
[J] J. Number Theory 28, No.2, 219-232 (1988). ISSN 0022-314X; ISSN 1096-1658/e

The author exhibits a graded algebra of hypergeometric functions and shows how to canonically identify it with the graded algebra of modular forms for the full modular group SL(2,${\bbfZ})$. He also shows how Dedekind's eta-function is related to the square root of a hypergeometric function and gives yet another simple proof of its functional equation.
[A.Venkov]

MSC 2000:: *11F11 Modular forms, one variable
33C05 Classical hypergeometric functions

Keywords: Mellin transforms; special values of Dirichlet series; integrals of hypergeometric functions; graded algebra of hypergeometric functions; graded algebra of modular forms; Dedekind's eta-function; functional equation

Cited in: Zbl 1034.11031

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