The Riemann Zeta Function ζ(x): a Primer

Abstract

This chapter and the next one recall basic properties of the Riemann zeta function ζ(x) in very elementary terms. We do not try to compete with the many exhaustive texts on ζ(x) to which we refer the reader, e.g., [14, 26, 31, 48, 55, 57, 63, 84, 89, 101]. We mainly survey the basic facts, arguments, and formulae to the extent that they will serve later, to make this book reasonably self-contained. We also highlight the analytical, as opposed to the purely arithmetical, features because those play a major role throughout. This part can then be a tutorial to ζ(x) from an analytical angle. The end of this chapter also reviews the Dirichlet beta and Hurwitz zeta functions.