Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

Authors

Nathan C. Ryan, Bucknell UniversityFollow
Nils-Peter SkoruppaFollow
Fredrik Stroemberg

Publication Date

2012

Description

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

Journal

Mathematics of Computation

Volume

81

Issue

280

First Page

2361

Last Page

2376

Department

Mathematics

Publisher Statement

First published in Mathematics of Computation in Vol. 81, No. 280, Oct. 2012, published by the American Mathematical Society.

Link to Published Version

http://www.ams.org/journals/mcom/2012-81-280/S0025-5718-2012-02584-1/

Recommended Citation

Ryan, Nathan C.; Skoruppa, Nils-Peter; and Stroemberg, Fredrik. "Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two." Mathematics of Computation (2012) : 2361-2376.