Zeros of the zeta function, Riemann hypothesis and Mellin transform, some formulas

Hélène Charrière (1)

1 ICJ - Institut Camille Jordan

In this paper, we prove a formula, expressing, in terms of the psi function and of the Riemann zeta function, the non-trivial zeros of the Riemann zeta function, and, more generally, any analytic function of these zeros. The proof of this formula contains the demonstration of the Riemann hypothesis: all non-trivial zeros of zeta have real part 1/2. Two methods are used, one of them using the Mellin transform.

Mots clés: fonction zeta; transformation de Mellin

Domaines: Variables complexes [math.CV]

Hélène Charrière. Zeros of the zeta function, Riemann hypothesis and Mellin transform, some formulas. 2011. ⟨hal-00655618v1⟩