A factorization of the Selberg zeta function attached to a rank 1 space form
The purpose of this paper is to compare the Selberg zeta function for a cocompact discrete group acting on a rank 1 symmetric space with the regularized determinant of the resolvent operator. The main difficulty in this programme is the evaluation of a family of integrals which intervene in the calculations and the results. These are of the form \[ \int^ \infty_ 0t^{2n} (\text{sech}^ 2at) (b^ 2+t^ 2) (\log (b^ 2+t^ 2)-c) dt \] and it turns out that they can be evaluated in terms of standard functions, the most exotic of which is the Barnes' double-gamma function. The rest of the paper is devoted to deducing the consequences for the Selberg zeta-function, including its functional equation.
scientific article; zbMATH DE number 222000
scientific article