Functional equations for double series of Euler-Hurwitz-Barnes type with coefficients

YoungJu Choie; Kohji Matsumoto

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arXiv · 1403.1940

Functional equations for double series of Euler-Hurwitz-Barnes type with coefficients

YoungJu Choie·Kohji Matsumoto

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Abstract

We first survey the known results on functional equations for the double zeta-function of Euler type and its various generalizations. Then we prove two new functional equations for double series of Euler-Hurwitz-Barnes type with complex coefficients. The first one is of general nature, while the second one is valid when the coefficients are Fourier coefficients of a cusp form.

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YoungJu Choie, Kohji Matsumoto. 2014-03-08. Functional equations for double series of Euler-Hurwitz-Barnes type with coefficients. https://arxiv.org/abs/1403.1940

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