Moments of the Riemann zeta function and Eisenstein series—I

It is shown that if the parameters of an Eisenstein series on GL(2k) are chosen so that its (integrated) L-function is the 2kth moment of the Riemann zeta function, then the terms in its constant term agree with factors appearing in a conjectural formula for the 2kth moment of zeta by Conrey, Farmer, Keating, Rubinstein and Snaith. When k=1, an explanation for this phenomenon is found by deducing Oppenheimʹs generalization of the Voronoï summation formula from the Eisenstein series and representation theoretic considerations. The possibility of eliminating the problematical “arithmetic factor” is discussed.