Number Theory


Disproofs of Riemann's Hypothesis

Authors: Chun-Xuan Jiang

As it is well known, the Riemann hypothesis on the zeros of the ζ(s) function has been assumed to be true in various basic developments of the 20-th century mathematics, although it has never been proved to be correct. The need for a resolution of this open historical problem has been voiced by several distinguished mathematicians. By using preceding works, in this paper we present comprehensive disproofs of the Riemann hypothesis. Moreover, in 1994 the author discovered the arithmetic function Jn(ω) that can replace Riemann's ζ(s) function in view of its proved features: if Jn(ω) ≠ 0, then the function has infinitely many prime solutions; and if Jn(ω) = 0, then the function has finitely many prime solutions. By using the Jiang J2(ω) function we prove the twin prime theorem, Goldbach's theorem and the prime theorem of the form x2 + 1. Due to the importance of resolving the historical open nature of the Riemann hypothesis, comments by interested colleagues are here solicited.

Comments: 13 pages

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[v1] 5 Apr 2010

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