On Dirichlet Series and Petersson Products for Siegel Modular Forms

Siegfried Böcherer[1]; Francesco Ludovico Chiera[2]

  • [1] Universität Mannheim Fakultät für Mathematik und Informatik A5, 68131 Mannheim(Germany)
  • [2] Università “La Sapienza” di Roma Dipartimento di Matematica P. le A. Moro 2 00185 Rome (Italy)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 3, page 801-824
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Böcherer, Siegfried, and Chiera, Francesco Ludovico. "On Dirichlet Series and Petersson Products for Siegel Modular Forms." Annales de l’institut Fourier 58.3 (2008): 801-824. <http://eudml.org/doc/10335>.

@article{Böcherer2008,
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 $k \ge n/2$ has meromorphic continuation to $\mathbb\{C\}$. Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight $k\ge n/2$ may be expressed in terms of the residue at $s=k$ of the associated Dirichlet series.},
affiliation = {Universität Mannheim Fakultät für Mathematik und Informatik A5, 68131 Mannheim(Germany); Università “La Sapienza” di Roma Dipartimento di Matematica P. le A. Moro 2 00185 Rome (Italy)},
author = {Böcherer, Siegfried, Chiera, Francesco Ludovico},
journal = {Annales de l’institut Fourier},
keywords = {Rankin-Selberg method; Petersson product; non-cuspidal modular forms; invariant differential operators},
language = {eng},
number = {3},
pages = {801-824},
publisher = {Association des Annales de l’institut Fourier},
title = {On Dirichlet Series and Petersson Products for Siegel Modular Forms},
url = {http://eudml.org/doc/10335},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Böcherer, Siegfried
AU - Chiera, Francesco Ludovico
TI - On Dirichlet Series and Petersson Products for Siegel Modular Forms
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 3
SP - 801
EP - 824
AB - 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 $k \ge n/2$ has meromorphic continuation to $\mathbb{C}$. Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight $k\ge n/2$ may be expressed in terms of the residue at $s=k$ of the associated Dirichlet series.
LA - eng
KW - Rankin-Selberg method; Petersson product; non-cuspidal modular forms; invariant differential operators
UR - http://eudml.org/doc/10335
ER -

References

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