Correspondence among Eisenstein series E-2,E-1(tau,z), H-3/2(tau) and E-2(tau)

Abstract

One of the aims of this paper is to give a detail to produce a Jacobi- Eisenstein series of weight 2 and index 1, E-2,E-1 (tau,z) = -12 Sigma(n,r is an element of Zr2 less than or equal to 4n) H(4n - r(2))q(n) xi(r), whose Fourier expansions are the same type as those of E-k,E-1(tau, z), k > 3, by using Hecke trick. We also study a correspondence among three Eisenstein series E-2,E-1(tau, z), H-3/2 (tau) and E-2(tau) Moreover, we study that a correspondence between nonholomorphic Eisenstein series.