Asymptotics for the 2k-th moments of the Riemann zeta function have been conjectured by Conrey, Farmer, Keating, Rubinstein and Snaith. These show a striking parallel with certain Fourier coefficients of Eisenstein series on GL(2k). Even when k=1, this coincidence for the second moment requires an explanation which is found in the summation formula of Voronoi and Oppenheim, which can be gotten from a GL(2) Eisenstein series. A similar though only partially proved summation formula based on GL(2k) Eisenstein series will also be described. (Joint work with J. Beineke.)