The Hurwitz Zeta Function and the Lerch Zeta Function

Abstract

In this chapter we will discuss formulas we have developed for the evaluation of certain zeta functions. We will need them later for the numerical computation of the spectrum of the transfer operator. The implementations of these zeta functions are in a sense the heart of our computations, so we need to be very careful. Unfortunately we have found approximations of these zeta functions in the literature which are quite limited; this is the case especially for the Lerch zeta function. This is understandable, since these zeta functions are special functions, which compared to others are not used so often.