Explicit formula for the spherical image of the symplectic Hecke series of genus four

2006/06/20 by Kirill Vankov, Vankov, Kirill
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Finite Group Theory Research #math.NT #msc:11F60

paper · pdf · doi:10.48550/arxiv.math/0606492

arxiv created 2006/09/29 · arxiv updated 2009/12/01

Abstract

We obtain an explicit formula for the spherical image of the polynomial fraction conjectured by Shimura in 1963 for generating Hecke series in particular case of genus 4. As in our previous work we used the Satake spherical map for \rm Sp₄ and formulas by Andrianov. Key words: Hecke operators, Dirichlet series, Euler factorization, spherical map.

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