The Hadamard factorization of the Selberg zeta function on a compact Riemann surface

Abstract

The Selberg zeta function is decomposed into a canonical product over its zeros in analogy with the Hadamard product formula for the Riemann zeta function. The contribution from the trivial zeros contains the Barnes G-function, while the other zeros generate the Fredholm determinant of the laplacian. The result explains and extends some determinant calculations in string theory.