International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 21, Pages 3527-3537
A sequential Riesz-like criterion for the Riemann hypothesis
Departamento de Matemáticas, Instituto Venezolano de Investigaciones
Científicas, Apartado Postal 21827, Caracas 1020-A, Venezuela
Received 7 June 2005; Revised 18 August 2005
Copyright © 2005 Luis Báez-Duarte. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let . We prove that the Riemann hypothesis is equivalent to for all ; furthermore, we prove that implies that the zeros of are simple. This is closely related to M. Riesz's criterion which states that
the Riemann hypothesis is equivalent to as , for all .