Approximating the riemann zeta and related functions

Abstract

In this chapter we study the well-known function G, as well as some other functions that have the same zeros as the Riemann zeta function ξ(z) in the critical strip. To this end, we first derive a Fourier series expansion of G. Next, we use asymptotic methods to derive another function which also has the same zeros in the critical strip as ξ(z), but which lacks the extreme oscillatory behavior and extreme amplitude values that ξ(z) possesses, and which is therefore more suitable for computational purposes.