A possible novel approach to the Riemann Hypothesis (RH) by means of Generalized Zeta Functions related to an infinite set of numerical sequences generated by the Sieve of Eratosthenes

Riemann Hypothesis (RH) is one of the most important unresolved problems in mathematics. It is based on the observation that a link exists between the positions on the critical strip 0 < R(s) < 1, s E C, of the non-trivial zeroes in the Riemann's zeta function and the distribution of the primes in the succession of naturals. Riemann suggested that all of these infinitely many zeroes lie on the critical line R(s) = 1/2 , in such a way the distribution of the primes becomes the most regular possible. However, an important observation is that the succession of primes is the final result of an infinite number of steps of the well-known Sieve of Eratosthenes. This Report provides an overview of the Riemann's analysis, and finally gives some hints about a possible approach to the RH, which exploits the partial numerical successions provided by the Sieve procedure steps.