Timeline for More mysteries about the zeros of the Riemann zeta function
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2021 at 7:25 | vote | accept | Vincent Granville | ||
| Apr 17, 2021 at 6:08 | history | edited | Vincent Granville | CC BY-SA 4.0 |
added 5 characters in body
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| Jan 9, 2021 at 17:10 | history | edited | Vincent Granville | CC BY-SA 4.0 |
added 327 characters in body
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| Jan 5, 2021 at 18:46 | history | edited | Vincent Granville | CC BY-SA 4.0 |
I added this note: Interestingly, when $\sigma=\frac{1}{2}$ the orbit does not have a hole anymore as predicted, yet the error points are still distributed on a similar ring.
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| Jan 5, 2021 at 8:18 | history | edited | Vincent Granville | CC BY-SA 4.0 |
I added the section "more interesting results" featuring a generalization of RH very different from the current versions (not involving L-function), and spectacular plots for the orbit as well as the error when using only the first 200 terms in the series representing $\phi$
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| Jan 2, 2021 at 2:00 | comment | added | Vincent Granville | For convergence of the series mentioned in the Appendix, one might use the General Dirichlet Test as mentioned by Mark Viola in his answer to the following question: math.stackexchange.com/questions/1746711/…. Still, you need a plot like the second chart in my answer below, to be bounded, in order to apply that test. Proving that it is always bounded regardless of $\sigma$ and $t$ (the bound depending on these two variables) might not be very easy. | |
| Jan 1, 2021 at 21:47 | answer | added | Vincent Granville | timeline score: 2 | |
| Dec 31, 2020 at 5:48 | comment | added | Vincent Granville | Small note: for $\zeta(s)$, Mathematica uses $\pi/2$ rather than $-\pi/2$ in the definition of $\phi_2$. This does not change anything as far as finding the roots are concerned. My definition produces the complex conjugate of the result provided by Mathematica. | |
| Dec 29, 2020 at 18:36 | comment | added | Vincent Granville | I posted a question to ask when it is legit to perform the series rearrangements I did in the Appendix. For the cases tested so far, it appears to be legit based on numerical evidence. See mathoverflow.net/questions/379947/… | |
| Dec 29, 2020 at 3:18 | history | edited | Vincent Granville | CC BY-SA 4.0 |
I fixed an error in formula $(\star)$ in the appendix. The error did not have any impact on the final results, so the conclusions remain unchanged.
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| Dec 27, 2020 at 0:26 | history | edited | Vincent Granville | CC BY-SA 4.0 |
deleted 1 character in body
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| Dec 26, 2020 at 23:54 | history | edited | Vincent Granville | CC BY-SA 4.0 |
two typos in last 2 expressions at the very bottom
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| Dec 26, 2020 at 22:11 | history | edited | Vincent Granville | CC BY-SA 4.0 |
Added at the bottom: Appendix: simplified formula for $|\zeta(s)|^2$, when $\frac{1}{2}<\Re(s)<1$
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| Dec 24, 2020 at 10:24 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor Math Jaxing (bracket scaling)
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| Dec 24, 2020 at 10:24 | comment | added | Jan-Christoph Schlage-Puchta | This is another evidence for the fact that the Riemann zetafunction is something special: slightly disturbing the definition gives functions that have none of the interesting properties of $\zeta$. This is why in the past general complex analysis had surprisingly little success in proving interesting statements for $\zeta$. | |
| Dec 24, 2020 at 10:07 | history | asked | Vincent Granville | CC BY-SA 4.0 |