The Functions ζ(s) and L(s, χ)

Abstract

This chapter develops further properties of the Riemann zeta function ζ(s) and the Dirichlet L-functions L(s, χ) defined for σ > 1 by the series

$$\zeta (s) = \sum\limits_{n = 1}^\infty {\frac{1}{{{n^s}}}}$$

and

$$L(s,\chi ) = \sum\limits_{n = 1}^\infty {\frac{{\chi (n)}}{{{n^s}}}}$$

.