Riemann Hypothesis

Jul 2014
8
0
Taiwan
P: ζ(sᵢ)=0
Q: sᵢ=σ+it
R: t≠0
S: σ=1/2

A: P≡[Q≡(R≡S)]

It is that ζ(1/2)=0 if the Proposition A doesn't hold, but actually, ζ(1/2)≈-1.4603545; therefore RH does hold.
 

mathman

Forum Staff
May 2007
6,913
762
I am not sure what you are trying to say. However (using your notation) the Riemann hypothesis states that all zeroes for 0<σ<1 are on the line σ=1/2+it, not necessarily for t=0.
 

Country Boy

Math Team
Jan 2015
3,261
899
Alabama
I presume you mean "for 0< |σ|<1".