A New Class of Theta Function Identities in Two Variables
نویسندگان
چکیده
We describe a new series of identities, which hold for certain general theta series, in two completely independent variables. We provide explicit examples of these identities involving the Dedekind eta function, Jacobi theta functions, and various theta functions of Ramanujan. Introduction Let z ∈ H = {x+ yi : x, y ∈ R, y > 0} and for each x ∈ R set q = exp(2πixz) and e(x) = exp(2πix). The Dedekind eta-function is defined by η(z) = q ∞ ∏
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