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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

Citations:

Zbl 0304.10020
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References:

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