A second limit formula for higher rank twisted Epstein zeta functions and some applications

Abstract

In this paper, we give the second limit formula and an analogue of the Chowla-Selberg formula for the twisted Epstein zeta functions of rank n > 2. As an application, we compute the determinant of the Euclidean Laplacian on the space of asymmetrically automorphic functions on Rⁿ by using our second limit formula.