Convolution Dirichlet series and a Kronecker limit formula for   second-order Eisenstein series
  The classical Kronecker limit formula gives the constant term of the non-holomorphic Eisenstein series E(z,s) for SL(2,Z) at s=1 in terms of the Dedekind eta function. Here we compute the analagous formula for an Eisenstein series twisted by modular symbols (periods of weight two holomorphic cusp forms) for general Fuchsian groups of the first kind. 
Jay Jorgenson and Cormac O'Sullivan