Estimates for eigenvalues of Hecke operators on Siegel cusp forms.
Explicit Hecke series for symplectic group of genus 4
Shimura conjectured the rationality of the generating series for Hecke operators for the symplectic group of genus . This conjecture was proved by Andrianov for arbitrary genus , but the explicit expression was out of reach for genus higher than 3. For genus , we explicitly compute the rational fraction in this conjecture. Using formulas for images of double cosets under the Satake spherical map, we first compute the sum of the generating series, which is a rational fraction with polynomial coefficients....