On analytic properties of the standard zeta function attached to a vector-valued modular form.

We proof a Garrett–Böcherer decomposition of a vector-valued Siegel Eisenstein series E l , 0 2 of genus 2 transforming with the Weil representation of Sp 2 (Z) on the group ring C [ (L ′ / L) 2 ] . We show that the standard zeta function associated to a vector-valued common eigenform f for the Weil representation can be meromorphically continued to the whole s-plane and that it satisfies a functional equation. The proof is based on an integral representation of this zeta function in terms of f and E l , 0 2 . [ABSTRACT FROM AUTHOR]