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

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

2006-06-20

arxiv.org/abs/math/0606492v3

Mathematics

Number Theory

Scientific paper

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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