Rapporto di ricerca (Research report), 2021, ENG
Bruno Aiazzi; Stefano Baronti; Leonardo Santurri; Massimo Selva
IFAC-CNR, Area della Ricerca di Firenze, Sesto Fiorentino, Italy.
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.
Generalized Zeta Functions, Riemann Hypothesis, Sieve of Eratosthenes
Baronti Stefano, Aiazzi Bruno, Santurri Leonardo, Selva Massimo
ID: 461803
Year: 2021
Type: Rapporto di ricerca (Research report)
Creation: 2021-12-29 16:12:56.000
Last update: 2023-12-15 10:54:52.000
CNR institutes
External IDs
CNR OAI-PMH: oai:it.cnr:prodotti:461803