0 Members and 1 Guest are viewing this topic.

https://www.wolframalpha.com/input?i=plot+re+%28log%28%28zeta%280.49999%2B+s+i%29%29+%2F+%28Zeta%281-0.49999+%2B+s+i%29%29%29%29+from+-9+to+9Plotted symmetrically, it looks like the letter V. So, I'll just call it V function.

It turns out that Zeta (2 pi i) isn't exactly the same as Zeta (1+2 pi i).

A more accurate inflection curve has a slightly bigger imaginary number.https://www.wolframalpha.com/input?i=plot+re%28log%28zeta%28x%2B+2.002117+pi+i%29+%2F%28Zeta%281-x%2B+2.002117+pi+i%29%29%29%

Quote from: hamdani yusuf on 19/06/2024 06:47:57It turns out that Zeta (2 pi i) isn't exactly the same as Zeta (1+2 pi i).This plot shows where they become the same. https://www.wolframalpha.com/input?i=plot+re%28log%28+zeta%28i+x%29+%2Fzeta%281%2Bi+x%29+%29+%29+from+2+pi+to+2.00000002+piIt's close to 2.00000001 π

The plot below shows where the S function produces zero as output where the real part of input deviates from the critical line.https://www.wolframalpha.com/input?i=plot+re%28log%28zeta%280.5-10%5E-1%2Bi+x%29%2Fzeta%280.5%2B10%5E-1%2Bi+x%29%29%29+from+2.002032256+pi+to++2.00203229+pihttps://www.wolframalpha.com/input?i=plot+re%28log%28zeta%280.5-10%5E-4%2Bi+x%29%2Fzeta%280.5%2B10%5E-4%2Bi+x%29%29%29+from+2.002116+pi+to+2.0021179+piAnd manually make the plot.

Quote from: hamdani yusuf on 17/05/2024 05:14:38We get a nice full wave when the imaginary part is exactly 2*pihttps://www.wolframalpha.com/input?i=plot+re%28log%28zeta%28x%2B+2+pi+i%29+%2F%28Zeta%281-x%2B+2+pi+i%29%29%29%29from+0+to+1

We get a nice full wave when the imaginary part is exactly 2*pi