Spherical image of local Hecke series of genus four

Kirill Vankov (1)

1 IF - Institut Fourier

For the spherical image of a polynomial fraction, we obtain the explicit formula conjectured by Shimura in 1963 for generating Hecke series in the particular case of genus 4. As in our previous work, we use formulas due to Andrianov for the Satake spherical map.

Mots clés: Hecke operators; Dirichlet series; Euler factorization; spherical map

Domaines: Théorie des nombres [math.NT]

Kirill Vankov. Spherical image of local Hecke series of genus four. Matematicheskie Zametki / Mathematical Notes, 2007, 81 (5-6), pp.605 - 608. ⟨10.1134/S0001434607050045⟩. ⟨hal-01571086⟩