Interaction of Hecke–Shimura rings and zeta functions

An automorphic structure on a Lie group consists of Hecke–Shimura ring of an arithmetical 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 Hecke–Shimura rings of integral symplectic groups and integral orthogonal groups of integral positive definite quadratic forms.