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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 n / 2 has meromorphic continuation to . Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight k n / 2 may be expressed in terms of the residue at s = k of the associated Dirichlet series.

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