On \(L\)-functions for \(\text{GSp}(4) \times \text{GL}(2)\) and their special values. (English) Zbl 0770.11025

Furusawa, Masaaki

J. Reine Angew. Math. 438, 187-218 (1993).

The author considers the restriction of the Klingen type Eisenstein series on \(\text{GU}(2,2)\) to \(\text{GSp}(4)\). As result we obtain the new integral representation of the degree eight \(L\)-function for \(\text{GSp}(4) \times \text{GL}(2)\) which works for the holomorphic forms on \(\text{GSp}(4)\). Moreover, we obtain the special value result and the explicit functional equation for the case when both forms are holomorphic, full modular and of the same weight under a nonvanishing condition on certain Fourier coefficients.

Reviewer: M. Furusawa (Stanford)

MSC:

11F66	Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F67	Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11F70	Representation-theoretic methods; automorphic representations over local and global fields
22E55	Representations of Lie and linear algebraic groups over global fields and adèle rings
11F30	Fourier coefficients of automorphic forms

Keywords:

degree eight \(L\)-function; Klingen type Eisenstein series; integral representation; special value; explicit functional equation