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

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

2010-08-05

arxiv.org/abs/1008.0995v2

Mathematics

Number Theory

21 p. Corrections for the polar divisor are made, proofs for cusp forms and for real quadratic fields are added. New title

Scientific paper

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.

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