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

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.

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
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