Asymptotics of the Selberg Zeta function on the spin moduli space

Abstract

We prove a limited asymptotic expansion up to order $t^4\log t$ of the logarithmic derivative of the Selberg zeta function for the spin Dirac operator on compact surfaces for families of hyperbolic metrics degenerating towards complete hyperbolic metrics with cusps in a pinching process where the lengths $l_j(t)$ of certain disjoint simple closed geodesics converge smoothly to $0$ as $t\to 0$.