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On Dirichlet Series and Petersson Products for Siegel Modular Forms

Siegfried Böcherer; Francesco Ludovico Chiera — 2008

Annales de l’institut Fourier

We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree $n$ and weight $k \geq n / 2$ has meromorphic continuation to $ℂ$ . Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight $k \geq n / 2$ may be expressed in terms of the residue at $s = k$ of the associated Dirichlet series.

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