Elliptic Eisenstein series for PSL2(Z)

Abstract

Let be a Fuchsian subgroup of the first kind acting by fractional linear transformations on the upper half-plane, and let be the associated finite volume hyperbolic Riemann surface. Associated to any cusp of, there is the classically studied non-holomorphic (parabolic) Eisenstein series. In [11], Kudla and Millson studied non-holomorphic (hyperbolic) Eisenstein series associated to any closed geodesic on. Finally, in [9], Jorgenson and the first named author introduced so-called elliptic Eisenstein series associated to any elliptic fixed point of. In this article, we study elliptic Eisenstein series for the full modular group. We explicitly compute the Fourier expansion of the elliptic Eisenstein series and derive from this its meromorphic continuation.