A generalization of Kronecker's first limit formula to GL(n)

Abstract: Kronecker's first limit formula gives the polar and constant terms of the Laurent series expansion of the Eisenstein series for SL(2,Z) at s=1. In this article, we generalize the formula to certain maximal parabolic Eisenstein series associated to SL(n,Z) for n greater than or equal to 2. We also show how the generalized formula can be used to give the polar and constant terms of the Dedekind zeta function of any number field at s=1.