Timeline for Non trivial zeros of Riemann zeta function
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 16, 2021 at 23:42 | comment | added | Alexander Kalmynin | It is esentially the same as Balazard-Saias-Yor criterion, so probably not. | |
| Jun 16, 2021 at 23:34 | comment | added | user292590 | Is it somewhere proved apart from Balazard et al. that $A=C$ is equivalent to RH? | |
| Jun 16, 2021 at 23:31 | comment | added | Alexander Kalmynin | I already explained in the comment above what I mean by "not true". It is more like "not necessarily true, to our knowledge". I also think that the Riemann hypothesis is true, actually | |
| Jun 16, 2021 at 23:29 | comment | added | user292590 | can you please give a counterexample that $A\neq C$? I think that $A=C$. | |
| Jun 16, 2021 at 23:28 | comment | added | Alexander Kalmynin | The last formula in your question states that $A=C+C$. It is true and derivation is correct. | |
| Jun 16, 2021 at 23:26 | comment | added | user292590 | Thanks. Can you please elaborate on how we get $A=2C$? | |
| Jun 16, 2021 at 23:24 | comment | added | Alexander Kalmynin | Clarifying comment added. By "not true" above I mean "equivalent to the Riemann hypothesis, so is not contained in the linked paper and also not likely to be derived as easily as the formula from the paper" | |
| Jun 16, 2021 at 23:22 | history | edited | Alexander Kalmynin | CC BY-SA 4.0 |
added 999 characters in body
|
| Jun 16, 2021 at 23:05 | comment | added | user292590 | The truth of which formula is equivalent to the Riemann hypothesis? | |
| Jun 16, 2021 at 23:02 | comment | added | user292590 | Which formula is correct? | |
| Jun 16, 2021 at 23:01 | comment | added | user292590 | How is the sum in the left , $\sum_{|\alpha|<1,f(\alpha)=0} \log\frac{1}{|\alpha|^2}$ equal to $\frac{1}{2}$ times the sum $\sum_{-\pi/2<\arg(\rho)<\pi/2}\log\left|\frac{\rho}{1-\rho}\right| + \sum_{-\pi/2<\arg(\rho)<\pi/2}\log\left|\frac{\rho}{1-\rho}\right| $ | |
| Jun 16, 2021 at 22:55 | comment | added | Alexander Kalmynin | @Shyla No, your final formula is correct, it's equivalent to what is stated in the article you linked. However, the formula in the Question is not true. I mean, it's truth is actually equivalent to RH. Also it is not the formula from the article. | |
| Jun 16, 2021 at 22:50 | comment | added | user292590 | are you saying that $$\sum_{|\alpha|<1,f(\alpha)=0}\log \frac{1}{|\alpha|^2}=\frac{1}{2}\left(\sum_{-\pi/2<\arg(\rho)<\pi/2}\log\left|\frac{\rho}{1-\rho}\right|+ \sum_{-\pi/2<\arg(\rho)<\pi/2}\log\left|\frac{\rho}{1-\rho}\right| \right) $$? | |
| Jun 16, 2021 at 19:26 | history | edited | Alexander Kalmynin | CC BY-SA 4.0 |
added 1 character in body
|
| Jun 16, 2021 at 19:19 | history | edited | Alexander Kalmynin | CC BY-SA 4.0 |
added 2 characters in body
|
| Jun 16, 2021 at 19:12 | history | answered | Alexander Kalmynin | CC BY-SA 4.0 |