The zeta-function of sixth degree for Hermitian modular forms of genus 2. (Russian) Zbl 0609.10022

Gritsenko, V. A.

Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 154, 46-66 (1986).

Let F be a Hermitian modular form of genus 2 which is an eigenfunction for some Hecke operators. In the paper under review the zeta-function \(Z_ F(s)\) corresponding to F is investigated. For example the analytic continuation and functional equation for \(Z_ F(s)\) are proved by the method of A. N. Andrianov [Usp. Mat. Nauk 29, No.3(177), 43-110 (1974; Zbl 0304.10020)].

Reviewer: A.Venkov

MSC:

11F67	Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F27	Theta series; Weil representation; theta correspondences
11M35	Hurwitz and Lerch zeta functions

Keywords:

Hermitian modular form; Hecke operators; zeta-function; analytic continuation; functional equation

Citations:

Zbl 0304.10020