Interaction of the Hecke–Shimura Rings and Zeta Functions

Abstract

An automorphic structure on a Lie group consists of the Hecke–Shimura ring of an arithmetic discrete subgroup and a linear representation of the ring on an invariant space of automorphic forms given by Hecke operators. The paper is devoted to interactions (transfer homomorphisms) of the Hecke–Shimura rings of integral symplectic groups and integral orthogonal groups of integral positive definite quadratic forms. Bibliography: 10 titles.