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

2010/09/16 by Nathan C. Ryan, Ryan, Nathan, Nils-Peter Skoruppa +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1009.3198

openalex publication_date 2010/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Rankin convolution type Dirichlet series D_F,G(s) of Siegel modular\nforms F and G of degree two, which was introduced by Kohnen and the second\nauthor, is computed numerically for various F and G. In particular, we\nprove that the series D_F,G(s), which share the same functional equation\nand analytic behavior with the spinor L-functions of eigenforms of the same\nweight are not linear combinations of those. In order to conduct these\nexperiments a numerical method to compute the Petersson scalar products of\nJacobi Forms is developed and discussed in detail.\n

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