## An Expression For The Argument of ζ at Zeros on the Critical Line

**Authors:** Stephen Crowley

It is conjectured that argζ(1/2+i t_n)=S_n(t_n)=π(3/2-frac((ϑ(t_n))/π)-⌊g~^(-1)(n)⌋-n) where g~^(-1)(t)=(t ln(t/(2 π e)))/(2 π)+7/8 is the inverse of g~(n)=((8n-7)π)/(4 W((8n-7)/(8 e))) which accurately approximates the Gram points g(n) and that all of the non-trivial zeros of ζ, enumerated by n, are on the critical line. Therefore, if S(t)=S_n(t_n) then the exact transcendental equation for the Riemann zeros has a solution for each positive integer n which proves that Riemann's hypothesis is true since the counting function for zeros on the critical line is equal to the counting function for zeros on the critical strip if the transcendental equation has a solution for each n.

**Comments:** 6 Pages.

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### Submission history

[v1] 2016-12-09 14:26:11

[v2] 2016-12-14 20:32:01

[v3] 2017-03-08 18:56:06

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