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Torus periods of automorphic functions and the meromorphic continuation of related Dirichlet Series

We consider modular functions (i.e., the Eisenstein series and Hecke-Maass forms) for the group PSL(2,Z). We fix a quadratic number field E. This gives rise to twisted (by a Hecke character of the field E) periods of a modular function along the torus corresponding to E. We prove meromorphic continuation for a Dirichlet series generated by these twisted periods.

preprint2011arXivOpen access
Andre Reznikov
math.RTmath.NT
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Andre Reznikov

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