On the zeros of the Riemann Zeta function

Lazhar Fekih-Ahmed (1)

1 ENIT - Ecole Nationale d'Ingénieurs de Tunis

This paper is divided into two independent parts. The first part presents a new integral and series representation of the Riemaan zeta function. An equivalent formulation of the Riemann hypothesis is given and few results on this formulation are briefly outlined. The second part exposes a totally different approach. Using the new series representation of the zeta function of the first part, exact information on its zeros is provided based on Tauberian-like results.

Mots clés: Number Theory; Riemann Zeta function; Riemann Hypothesis

Domaines: Théorie des nombres [math.NT]

Lazhar Fekih-Ahmed. On the zeros of the Riemann Zeta function. 2010. ⟨hal-00476252v1⟩