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New Theories / Re: What makes Riemann's Hypothesis Hard to Prove?
« Last post by hamdani yusuf on Today at 13:22:36 »Y function guarantees that at the critical line, its output is always negative infinity, because on that line, s=1-s*. Consequently,In the critical strip, where 0<Re(s)<1, backslash function never cross zero more than once. The closest is when the imaginary part of s=2π.
Y(s) = Ln (ζ(s)-ζ(s)) = Ln(0) = -~
To prove Riemann's hypothesis, a further step is required. It needs to show that ζ(s)<>ζ(1-s*) when s<>1-s*.
This is where the backslash function can help.
B(s) = Ln (ζ(s) / ζ(1-s*)) = Ln(ζ(s)) - Ln(ζ(1-s*))
Violation of Riemann's hypothesis requires that backslash function crosses zero more than once, presumably at very high imaginary part.
But it's contradictory to our observation that the real part of backslash function is even more stable at higher imaginary part.
https://www.wolframalpha.com/input?i=plot+%28log%28%28zeta%28x%2B999999999+i%29%29+%2F+%28Zeta%281-x%2B+999999999+i%29%29%29%29from+0+to+1