## 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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