## ABSTRACT

CHAPTER 2

2.1. Introduction

The table of integrals [35] contains a large variety of definite integrals that involve the Riemann zeta function

(2.1.1) ζ(s) = ∞∑ n=1

ns .

The series converges for Re s > 1. This is a classical function that plays an important role in the distribution

of prime numbers. The reader will find in [27] a historical description of the fundamental properties of ζ(s). The textbook [19] presents interesting information about the major open question related to ζ(s): all its non-trivial zeros are on the vertical line Re s = 12 . This is the famous Riemann hypothesis.