An Extension of the Chowla-Selberg Formula Useful in Quantizing with the Wheeler-De Witt Equation

Details An Extension of the Chowla-Selberg Formula Useful in Quantizing with the Wheeler-De Witt Equation An Extension of the Chowla-Selberg Formula Useful in Quantizing with the Wheeler-De Witt Equation

1994-02-28

arxiv.org/abs/hep-th/9402155v2

J.Phys. A27 (1994) 3775-3786

Physics

High Energy Physics

High Energy Physics - Theory

14 pages (small typo errors corrected and 2page improvement of physical applications), LaTeX file, UB-ECM-PF 94/7

Scientific paper

10.1088/0305-4470/27/11/027

The two-dimensional inhomogeneous zeta-function series (with homogeneous part of the most general Epstein type): \[ \sum_{m,n \in \mbox{\bf Z}} (am^2+bmn+cn^2+q)^{-s}, \] is analytically continued in the variable $s$ by using zeta-function techniques. A simple formula is obtained, which extends the Chowla-Selberg formula to inhomogeneous Epstein zeta-functions. The new expression is then applied to solve the problem of computing the determinant of the basic differential operator that appears in an attempt at quantizing gravity by using the Wheeler-De Witt equation in 2+1 dimensional spacetime with the torus topology.

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