On Dirichlet Series and Petersson Products for Siegel Modular Forms

Abstract

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 ℂ. 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.

Locations

• French digital mathematics library (Numdam) - View - PDF
• Annals of the Fourier Institute (Institut Fourier) - View - PDF
• Annales de l’institut Fourier - View - PDF