Timeline for Zeroes of real and imaginary parts of $\zeta(1+it)$ separately (if any for $t>1$ say)
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 12, 2017 at 21:24 | comment | added | TPTW | @juan Are other zeroes of Re and/or Im zeta-dash(1+it) possible, not arising in the way you describe, or does it capture all of them ? How accurate an estimate of their number in [1,T] do you think is possible ? | |
| May 12, 2017 at 21:05 | comment | added | TPTW | @juan V. many thanks juan. I knew about zeroes zeta-dash from Titchmarsh but yr research on the x-ray quite new to me and v.interesting. | |
| May 12, 2017 at 7:45 | comment | added | juan | @TPTW There are many zeros o f $\zeta'(s)$ with real part $>1$. For each one of these zeros there are two zeros of $\Re \zeta'(1+it)$ and $\Im\zeta'(1+it)$. For the derivative there are parallel real and imaginary lines (to the real axis) separated by $\pi/\log2$. Each one of these parallel lines gives a zero of $\Re \zeta'(1+it)$ or $\Im\zeta'(1+it)$ respectively. The x-ray of $\zeta'(s)$ show this, but I have not published this. | |
| May 11, 2017 at 23:46 | comment | added | TPTW | May I ask further, the two papers quoted not seeming to go into any detail about the same question for zeta-derivative(1+it), whether similar facts exist for this ? Arises out of question 'where does d/dt(|zeta(1+it)|^2) =0' ? | |
| May 11, 2017 at 22:36 | comment | added | TPTW | Very grateful to Sylvain, Stopple, Juan for their authoritative responses. | |
| May 11, 2017 at 7:54 | answer | added | juan | timeline score: 1 | |
| May 10, 2017 at 23:37 | comment | added | Sylvain JULIEN | Haseo Ki and Steven M. Gonek are writing a paper on pair correlation of zeroes of the real part of $\zeta$. | |
| May 10, 2017 at 23:32 | answer | added | Stopple | timeline score: 6 | |
| May 10, 2017 at 21:30 | history | edited | Stopple | CC BY-SA 3.0 |
tag added, TeX added
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| May 10, 2017 at 21:00 | review | First posts | |||
| May 10, 2017 at 21:19 | |||||
| May 10, 2017 at 20:58 | history | asked | TPTW | CC BY-SA 3.0 |