An extension of the Chowla-Selberg formula useful in quantizing with the Wheeler-De Witt equation

E Elizalde
1994 Journal of Physics A: Mathematical and General  
The two-dimensional inhomogeneous zeta-function series (with homogeneous part of the most general Epstein type): m,n∈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
more » ... tempt at quantizing gravity by using the Wheeler-De Witt equation in 2+1 dimensional spacetime with the torus topology.
doi:10.1088/0305-4470/27/11/027 fatcat:wmhnkl7pmbdbbhheh7fgaowzza