Timeline for Are all zeros of $\Gamma(s) \pm \Gamma(1-s)$ on a line with real part = $\frac12$ ?
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
replaced http://dl.dropbox.com/ with https://dl.dropbox.com/
|
|
| Apr 12, 2012 at 13:25 | comment | added | juan | yes I know it. But here the lines are very regular in xi not. | |
| Apr 12, 2012 at 12:47 | comment | added | joro | The x-ray of Riemann xi is very similar to your plot: s14.postimage.org/462qtowbl/riemann_xi.png | |
| Apr 12, 2012 at 12:41 | comment | added | joro | The plot (figure) is in the answer now, if you don't see it reload the page. | |
| Apr 12, 2012 at 11:23 | comment | added | juan | I do not understand you. It would be nice to have it in the answer. But here we have only the link, but not the figure. (I am not English speaker). | |
| Apr 12, 2012 at 9:01 | comment | added | joro | Included the plot in your answer, rollback if you don't want it in the answer. | |
| Apr 12, 2012 at 8:57 | history | edited | joro | CC BY-SA 3.0 |
Included juan's plot in his answer
|
| Apr 12, 2012 at 7:41 | comment | added | juan | Here we have the x-ray of Γ(x)−Γ(1−x) on the rectangle (−12,12)×(−12,12) img src = dl.dropbox.com/u/23924184/gammajoro1.png | |
| Apr 12, 2012 at 7:32 | history | edited | juan | CC BY-SA 3.0 |
deleted 72 characters in body
|
| Apr 11, 2012 at 7:14 | comment | added | joro | Juan, if you want an image included in your answer post an URL and i will try to edit the question. | |
| Apr 11, 2012 at 5:19 | comment | added | joro | juan, you can post images (possibly unless you don't have enough reputation). The format is HTML, i.e. write <img src="server/file.gif"> in your answer. The x-rays i found are at drememi.ludost.net/gamma1.png and drememi.ludost.net/gamma2.png | |
| Apr 10, 2012 at 16:24 | comment | added | juan | Of course the real zeros are symmetric with respect to 0.5 so that there are zeros near $-3$, $-4$, $\dots$ | |
| Apr 10, 2012 at 16:20 | history | edited | juan | CC BY-SA 3.0 |
added 24 characters in body
|
| Apr 10, 2012 at 16:11 | comment | added | juan | Apparently I can not post here a plot. The x-ray gives little doubt that the zeros of $\Gamma(s)-\Gamma(1-s)$ are the ones with real part $1/2$ that appeared computed in this question. The complex at $-1.69-0.30 i$ its complex conjugate the symmetrical of this with respect the critical line $2.69+0.30i$ and its complex conjugate. And then the real zeros one at $0.5$. The others real zeros can be obtained best from a real plot of the function. In the x-ray this zeros, that are very near the poles at $4$, $5$, $\dots$, can not be seen since they are contained in very short lines. | |
| Apr 9, 2012 at 19:39 | comment | added | juan | With mpmath I check also this zero. I think now that my parenthesis "(with some effort)" contains an error. :-/ What it is clear is that the real zeros are those of the function given. But the behavior of this function for t complex is really not simple. I will try to do an X-ray of this function. Later we will try to post it. If I know how to do it. | |
| Apr 9, 2012 at 9:26 | comment | added | joro | juan, how do you explain the approximations of zeros in my answer with precision 100 checked in pari, sage and maple? Have I misunderstood the question? | |
| Mar 26, 2012 at 8:37 | history | edited | juan | CC BY-SA 3.0 |
added 76 characters in body; deleted 7 characters in body; added 8 characters in body
|
| Mar 26, 2012 at 8:19 | history | answered | juan | CC BY-SA 3.0 |
