Titre : The Riemann zeta function or the navel of mathematics to deal with complexity (1) 

Auteurs : Philippe Riot,  

Revue : Entropy: Thermodynamics – Energy – Environment – Economy  

Numéro : Special issue LILA 2 

Volume : 5 

Date : 2024/05/16 

DOI : 10.21494/ISTE.OP.2024.1157 

ISSN : 2634-1476 

Résumé : The Riemann zeta function is identified on the one hand as a substitute for the equality predicate and on the other hand as a model of continuity. Thanks to this second interpretation, Riemann’s conjecture addressing the distribution of non-trivial zeros of this function is not resolved here, it is dissolved in the sense that its statement turns out to be equivalent to an essential axiom of the forcing technique, namely the Martin’s axiom. For practical reasons of length of the text, the restitution of the study of this function is divided into two parts. The first focuses on the interpretation of the zeta function as a logical interpolator while the second part will be devoted to the topological and ordinal study to understand the meaning of the Riemann statement concerning the location of nontrivial zeros of this function. The interpretation of the function resulting from the study, the main conclusions of which are presented in both articles, explains the central role played by this function not only in mathematics, but also in many other scientific fields, in particular to study the behavior of complex systems. 

Éditeur : ISTE OpenScience