## Andrianov’s $$L$$-functions associated to Siegel wave forms of degree two.(English)Zbl 0837.11026

The author considers a kind of Maaß wave form $$F$$ on the Siegel half space of degree 2. Assume that $$F$$ is a cusp form and simultaneous Hecke eigenform. Then the Andrianov $$L$$-function $$L_F(s)$$ attached to $$F$$ is investigated. $$L_F (s)$$ possesses an analytic continuation as an entire function and satisfies a functional equation under $$s \mapsto - 2 - s$$. These results generalize A. N. Andrianov’s results [Russ. Math. Surv. 29, No. 3, 45-116 (1974); translation from Usp. Mat. Nauk 29, 43-110 (1974; Zbl 0304.10020)] on holomorphic Siegel modular forms of degree 2.
Reviewer: A.Krieg (Aachen)

### MSC:

 11F46 Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms 11F66 Langlands $$L$$-functions; one variable Dirichlet series and functional equations

Zbl 0304.10020
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### References:

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