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

Kirill Vankov

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

Kirill Vankov

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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 ${\rm Sp}_4$ and formulas by Andrianov. Key words: Hecke operators, Dirichlet series, Euler factorization, spherical map.

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Kirill Vankov. 2006-09-29. Explicit formula for the spherical image of the symplectic Hecke series of genus four. https://arxiv.org/abs/math/0606492

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