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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Numerical computation of a certain Dirichlet series attached to Siegel modular forms of degree two


Authors: Nathan C. Ryan, Nils-Peter Skoruppa and Fredrik Strömberg
Journal: Math. Comp. 81 (2012), 2361-2376
MSC (2010): Primary 11F46, 11F66; Secondary 11F27, 11F50
Published electronically: February 20, 2012
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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.


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Additional Information

Nathan C. Ryan
Affiliation: Department of Mathematics, Bucknell University, Lewisburg, Pennsylvania 17837
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

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02584-1
PII: S 0025-5718(2012)02584-1
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.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.