**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 J_{n}(ω) that can replace Riemann's ζ(s) function in view of
its proved features: if J_{n}(ω) ≠ 0, then the function has infinitely many
prime solutions; and if J_{n}(ω) = 0, then the function has finitely many
prime solutions. By using the Jiang J_{2}(ω) function we prove the twin
prime theorem, Goldbach's theorem and the prime theorem of the form
x^{2} + 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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