Extended Gauss AGM and corresponding Picard modular forms
نویسندگان
چکیده
The latter theorem shows the relation of the (coefficients of the realized) elliptic curves corresponding to two isogenous torus C/Z + τZ and C/Z + 2τZ. So in general this theorem is referred as the isogeny formula for the Jacobi theta constants. Any way these two theorems are telling us a very interesting story concerned with AGM, periods of algebraic varieties, hypergeometric functions and modular forms at a same time. But still now there is no sufficiently nice generalization for it. In this article we show an extended story of Gauss AGM to two variables case by using Picard modular forms for Q( √ −1) studied by Matsumoto [Mat1] which is coming from one of the Terada and Deligne-Mostow list.
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