Timeline for Question on coefficient of $\exp(H_n).\log(H_n)$ in Lagarias equivalence of RH
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 13, 2022 at 2:21 | comment | added | npcr | As I understood from this discussion, if RH is false, it can be provably false because of Robin-Ramanujan inequalities | |
| May 3, 2022 at 19:46 | comment | added | GH from MO | @EGME I don't think it is known that RH is decidable within ZFC. Note also that the solvability of any diophantine equation can be formulated within the theory of complex numbers, and there are diophantine equations whose solvability is not decidable within ZFC (assuming ZFC is consistent). | |
| May 3, 2022 at 15:11 | comment | added | EGME | RH is a complex number problem. The theory of complex numbers is complete,, therefore there is either a proof of RH or a proof of its negation (analytic). On the other hand, it could be independent in Peano Arithmetic | |
| Aug 12, 2021 at 19:57 | comment | added | GH from MO | @SylvainJULIEN: If ZFC is consistent, then there is no algorithm that could tell about every statement in ZFC whether it is decidable or not from the ZFC axioms. | |
| Aug 12, 2021 at 19:53 | comment | added | GH from MO | @PrashanthNCR: The third display can be strengthened by including a factor of $e^\gamma$ in the denominator. Note that $e^\gamma$ exceeds $1$. In fact this factor could be enlarged slightly, because in Robin's bound there is a constant $0.6482$ present in front of the fraction. I omitted these constants for elegance of presentation. | |
| Aug 12, 2021 at 19:44 | comment | added | Sylvain JULIEN | Is there a way to check if the attempt of proof of some statement (not necessarily RH) is decidable from ZFC axioms? | |
| Aug 12, 2021 at 19:20 | comment | added | npcr | Thanks for the explanation @GHfromMO . It's very clear for me now. Also, shouldn't there be $\exp(\gamma)$ in the denominator of the fraction on the RHS ? Your next statement that it tends to zero is still valid as $\exp(\gamma)$ is a constant, but I'm just making sure my understanding is correct as I don't really have a math background. | |
| Aug 12, 2021 at 19:14 | vote | accept | npcr | ||
| Aug 12, 2021 at 18:56 | comment | added | Charles | +1. Prashanth, this is the answer to accept. | |
| Aug 12, 2021 at 18:09 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Aug 12, 2021 at 18:00 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Aug 12, 2021 at 17:52 | history | answered | GH from MO | CC BY-SA 4.0 |