A FORMAL THEORY OF EISENSTEIN SERIES

The definition of the Eisenstein series E (Z, s, k, Gamma) on the symplectic and unitary groups G is well-known. We introduce a series E (Z, lambda) whose construction involves a 5-tuple {G, P, M, W, epsilon} satisfying certain conditions. We prove that, if lambda: M(nx2n) n (E) --> C is a locally-constant function, then the series E (Z, lambda) is a finite linear combination of G-transforms of the Eisenstein series E (Z, s k, Gamma) whose coefficients are products of certain Hecke L-functions.