Open AccessRiemann Hypothesis
Author(s) -
Joseph E Brierly
Publication year - 2022
Language(s) - English
DOI - 10.47363/jpsos/2022(4)161
Subject(s) - riemann zeta function , riemann hypothesis , mathematics , pure mathematics , function (biology) , simple (philosophy) , arithmetic zeta function , character (mathematics) , particular values of riemann zeta function , calculus (dental) , prime zeta function , philosophy , epistemology , geometry , medicine , dentistry , evolutionary biology , biology
In 1859 Bernard Riemann hypothesized that the zeros of the Zeta function only can occur on either the x axis or the line ½+ti for all values of t. This article explains why Riemann’s hypothesis (RH) is correct. for a complex numbers. The basic Zeta function Z(s) above was shown to be analytic for the real part of s greater than 1. Several other forms of the Zeta function were subsequently determined [1]. Attempts to verify RH has attracted many to verify the RH since 1859 without success. This article gives a proof that the RH is correct. [2] gives an extensive list of references of research articles in its list of references demonstrating the historical interest in the character of the Zeta Function. The proof of the RH is remarkably simple but requires a subtle proof given in this article.