Journal of the Ramanujan Mathematical Society

Volume 39, Issue 4, December 2024 pp. 359–368.

A generalization of Kronecker's first limit formula

Authors: Amod Agashe
Author institution:Department of Mathematics, Florida State University, Tallahassee, Florida 32306, U.S.A.

Summary: 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, which in turn can be used to find expressions for the polar and constant terms of partial or Dedekind zeta functions of quadratic fields. In this article, we generalize the formula to certain maximal parabolic Eisenstein series associated to SL(n,ℤ) for n ∉ 2. We also show how the generalized formula can be used to find expressions for the polar and constant terms of partial or Dedekind zeta functions of arbitrary number fields at s = 1.

Contents Full-Text PDF