Timeline for Behaviour of $\zeta(1-it)/\zeta(1+it)$?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 3, 2015 at 8:10 | vote | accept | Tian An | ||
| Sep 26, 2015 at 12:22 | comment | added | მამუკა ჯიბლაძე | Oh sorry I just did not notice the word "argument" :D | |
| Sep 26, 2015 at 12:12 | comment | added | juan | @ მამუკა ჯიბლაძე @paul garrett No, I mean $\sigma=1$, I speak of the function $\arg \zeta(1+i t)$. This is real analytic vanishes at $c T$ points (think on the x-ray, but this can be proved ). Also we know how to compute the probabilities I speak about. | |
| Sep 26, 2015 at 11:57 | comment | added | მამუკა ჯიბლაძე | @juan You mean $\sigma=\frac12$ I believe? | |
| Sep 26, 2015 at 10:30 | comment | added | juan | In what sense use you the word regular? "... the argument of zeta of the line $\sigma=1$ becomes very regular". Of course it is a real analytic function. But, for $0<t<T$ there are $cT$ points where it is $=0$. But it is not bounded. The probability to be greater than $2\pi$ being very small, to be $\ge 4\pi$ almost incredibly small, and so on. I will not call this behavior "regular". | |
| Sep 25, 2015 at 23:41 | comment | added | Tian An | +1 Thank you for the very nice reference! | |
| Sep 25, 2015 at 23:26 | history | answered | paul garrett | CC BY-SA 3.0 |