Numerical computation of a certain Dirichlet series attached to Siegel modular forms of degree two
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- by Nathan C. Ryan, Nils-Peter Skoruppa and Fredrik Strömberg PDF
- Math. Comp. 81 (2012), 2361-2376 Request permission
Abstract:
The Rankin convolution type Dirichlet series $D_{F,G}(s)$ 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 $D_{F,G}(s)$, 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.References
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Additional Information
- Nathan C. Ryan
- Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
- MR Author ID: 807431
- ORCID: 0000-0003-4947-586X
- Email: nathan.ryan@bucknell.edu
- Nils-Peter Skoruppa
- Affiliation: Fachbereich Mathematik, Universität Siegen, Germany
- Email: nils.skoruppa@uni-siegen.de
- Fredrik Strömberg
- Affiliation: Fachbereich Mathematik, TU-Darmstadt, Germany
- Email: stroemberg@mathematik.tu-darmstadt.de
- Received by editor(s): August 12, 2010
- Received by editor(s) in revised form: June 7, 2011
- Published electronically: February 20, 2012
- Additional Notes: This project was supported by the National Science Foundation under FRG Grant No. DMS-0757627, the authors also made use of hardware provided by DMS-0821725.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 2361-2376
- MSC (2010): Primary 11F46, 11F66; Secondary 11F27, 11F50
- DOI: https://doi.org/10.1090/S0025-5718-2012-02584-1
- MathSciNet review: 2945160