## Number Theory   ## Proof of Riemann Hypothesis

Authors: Toshiro Takami

Let a be real number of 0< a <1.  (1)= cos[x*ln1]/1^a – cos[x*ln2]/2^a + cos[x*ln3]/3^a – cos[x*ln4]/4^a + cos[x*ln5]/5^a............  (2)= sin[x*ln1]/1^a – sin[x*ln2]/2^a + sin[x*ln3]/3^a – sin[x*ln4]/4^a + sin[x*ln5]/5^a............. Then, at this time,  The imaginary solution of the equation (1)^2+(2)^2=0 exists only when a = 0.5. x is an infinite non-trivial zero.  At the same time satisfying (1) and (2) is x, that is, an infinitely present non-tribial zero. (1) is \sum_{n=1}^{infty} [cos(x*ln(2n-1))/(2n-1)^0.5)- cos(x*ln(2n)/(2n)^0.5)] =0 (2) is \sum_{n=1}^{infty} [sin(x*ln(2n-1))/(2n-1)^0.5) - sin(x*ln(2n)/(2n)^0.5)] =0

Comments: 9 Pages. serios mistake consist, re-load-up

### Submission history

[v1] 2019-02-28 04:36:53 (removed)
[v2] 2019-02-28 17:46:37 (removed)
[v3] 2019-03-04 13:56:54 (removed)
[v4] 2019-03-08 02:53:41
[v5] 2019-03-08 17:19:49
[v6] 2019-03-10 05:08:41
[v7] 2019-03-11 02:08:38
[v8] 2019-03-12 19:14:08
[v9] 2019-03-13 17:36:31