Definition of ζ(s), Z(t) and basic notions
1.1 The basic notions
The classical Riemann zeta-function
admits analytic continuation to . It is regular on except for a simple pole at s = 1. The product representation in (1.1) shows that ζ (s) does not vanish for σ > 1. The Laurent expansion of ζ(s) at s = 1 reads
where the so-called Stieltjes constants ...