Li's criterion for Epstein zeta functions, generalization of Kronecker's limit formula and the Gauss problem

Abstract

In this paper, we first investigate the Li criterion for the Riemann hypothesis for a class of Epstein zeta functions. Then, we derive some interesting consequences for the class number of a quadratic imaginary number field K using Kronecker's limit formula and Hecke's formulation for the meromorphic continuation of the Dedekind zeta function ζK.