科研之友
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摘要
In this paper we show a two-dimensional variant of the classical Jacobi formula between a theta constant and the Gauss hypergeometric function. We use the family of algebraic curves given in the form w(4) = z(2)(z - 1)(2)(z - lambda(1))(z - lambda(2)) with two complex parameters lambda(1), lambda(2) and the modular functions for them. Our result is an exact extension of the classical formula that is contained as a degenerated case. As an application we give a new proof for the extended Gauss arithmetic geometric mean theorem in two variables obtained by Koike and Shiga (J. Number Theory 128 (2008), 2029-2126).
- 出版日期2011-3
