CONTRIBUTION OF NON INTEGER INTEGRO-DIFFERENTIAL OPERATORS (NIDO) TO THE GEOMETRICAL UNDERSTANDING OF RIEMANN'S CONJECTURE-(I)

摘要

Advances in fractional analysis suggest a new way for the understanding of Riemann's conjecture. This analysis shows that any divisible natural number may be related to phase angles naturally associated with a certain class of non integer integro differential operators. It is shown that the subset of prime numbers is most likely related to a phase angle of ±π/4 to a 1/2-order differential equations and with their singularities. Riemann's conjecture asserting that, if s is a complex number, the non trivial zeros of zeta function 1/ζ(s) = sum from n=1 to ∞ (μ(n))/n~s in the gap [0,1], is characterized by s = 1/2 (1+2iθ), can be understood as a consequence of the properties of 1/2-order fractional differential equations on the prime number set. This physical interpretation suggests opportunities for revisiting flitter and cryptographic methodologies.