Torus periods of Maass forms and meromorphic continuation of 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 form along the corresponding to E torus. We prove meromorphic continuation for a Dirichlet series generated by these twisted periods.