Contribution of Non Integer Integro-Differential Operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II)

Alain Le Méhauté (1) , Abdelaziz El Kaabouchi (1) , Laurent Nivanen (1)

1 ISMANS CESI - Institut Supérieur des Mécaniques et Matériaux Avancés

Advances in fractional analysis suggest a new way for the physics understanding of Riemann's conjecture. It asserts that, if s is a complex number, the non trivial zeros of zeta function in the gap [0,1], is characterized by . This conjecture can be understood as a consequence of 1/2-order fractional differential characteristics of automorph dynamics upon opened punctuated torus with an angle at infinity equal to . This physical interpretation suggests new opportunities for revisiting the cryptographic methodologies.

Mots clés: Fractal; Algebraic structures and number theory; Differential geometry and topology; Statistical mechanics; Fractal analysis; Signal treatment; Cryptography

Domaines: Topologie géométrique [math.GT]; Variables complexes [math.CV]

Alain Le Méhauté, Abdelaziz El Kaabouchi, Laurent Nivanen. Contribution of Non Integer Integro-Differential Operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II). 2006. ⟨hal-00069527⟩