Abstract
We consider the resummation of the semiclassical Selberg zeta function for quantized maps on compact phase space, specifically the quantized Baker's map. In particular, we demonstrate that the semiclassical periodic-orbit expansion leads to an effectively finite polynomial for the spectrum of the quantum map. However, the coefficients are not self-inverse (as required by unitarity). An extension of the semiclassical approximation by including corrections due to the discontinuities of the classical map improves the situation. The improved polynomial is closer to being self-inverse but the eigenphases remain complex. Slightly better results are obtained if the functional equation is imposed on the semiclassical expansion.