Timeline for Periodicity in the distribution of non-trivial zeros of the Riemann Zeta function
Current License: CC BY-SA 4.0
17 events
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| Aug 8, 2022 at 8:50 | comment | added | juan | @Salvo The figures of the partial sums $\sum_{k=1}^n e^{ik+i\gamma_k}$ are very similar to the ones in the book by Montgomery, I have done it for $1\le n\le 100000$. Impressive. | |
| Aug 7, 2022 at 21:24 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Aug 7, 2022 at 21:03 | comment | added | juan | @Salvo I confirm your plot. There are other jumps, the next one between $10000<n<15000$ and other between $[50000,60000]$. Perhaps $\sum_{k=1}^n e^{ikx+i\gamma_k}$ behaves as the sum considered by H. Montgomery in \emph{Ten Lectures on the Interface between Number Theory and Harmonic Analysis} p. 45--60. | |
| Aug 7, 2022 at 18:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jul 8, 2022 at 17:25 | answer | added | Steven Clark | timeline score: 1 | |
| Jul 7, 2022 at 22:30 | comment | added | Salvo | @Stopple re-edited. | |
| Jul 7, 2022 at 22:29 | history | edited | Salvo | CC BY-SA 4.0 |
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| Jul 5, 2022 at 17:34 | comment | added | Stopple | Usually $\rho_n$ denotes the complex nontrivial zeros, written $\beta_n+i\gamma_n$; on the Riemann hypothesis $\beta_n=1/2$. With this notation $\sin(\rho_n)$ and thus $\tau(n)$ are complex numbers, not real valued. Either your $\tau(n)$ is actually the real part of your sum, or you are evaluating $\sin(\gamma_n)$, not $\sin(\rho_n)$. | |
| Jul 2, 2022 at 15:16 | comment | added | jeq | @AmirSagiv: One needs 10 reputation points before being allowed to embed a figure. See meta.stackexchange.com/questions/75491/…. | |
| S Jul 2, 2022 at 6:09 | history | suggested | jeq | CC BY-SA 4.0 |
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| Jul 2, 2022 at 4:48 | comment | added | Amir Sagiv | Can you include the figure in the post, not as a link? | |
| Jul 2, 2022 at 0:35 | review | Suggested edits | |||
| S Jul 2, 2022 at 6:09 | |||||
| Jul 1, 2022 at 22:04 | comment | added | Salvo | @Stopple edited, thanks. | |
| Jul 1, 2022 at 22:03 | history | edited | Salvo | CC BY-SA 4.0 |
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| Jul 1, 2022 at 22:01 | comment | added | Stopple | Does $\rho_n$ denote the real part of the zero, or the zero itself? If the former, (many more than) the first $10^n$ have real part 1/2; why not just write that? If the latter, I don't understand the point of your first sentence. | |
| S Jul 1, 2022 at 21:50 | review | First questions | |||
| Jul 2, 2022 at 4:48 | |||||
| S Jul 1, 2022 at 21:50 | history | asked | Salvo | CC BY-SA 4.0 |