Timeline for Irrationality of the values of the prime zeta function
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| S Oct 28, 2018 at 16:00 | history | bounty ended | CommunityBot | ||
| S Oct 28, 2018 at 16:00 | history | notice removed | CommunityBot | ||
| Oct 21, 2018 at 7:31 | comment | added | Klangen | @GerryMyerson I am well aware of that. If there isn't any, I accept that as an answer too. | |
| Oct 20, 2018 at 22:00 | comment | added | Gerry Myerson | Just because you are looking for recent research, doesn't mean that there has actually been any. | |
| Oct 20, 2018 at 14:24 | history | edited | Martin Sleziak |
added (nt.number-theory) so that the question has a top-level tag - if there are more suitable choices, please edit the tags further; https://meta.mathoverflow.net/questions/1457/why-are-mo-tags-formatted-as-they-are
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| Oct 20, 2018 at 14:08 | history | edited | Klangen | CC BY-SA 4.0 |
added 217 characters in body
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| S Oct 20, 2018 at 14:06 | history | bounty started | Klangen | ||
| S Oct 20, 2018 at 14:06 | history | notice added | Klangen | Authoritative reference needed | |
| Oct 18, 2018 at 13:08 | comment | added | Klangen | @GerryMyerson Thank you for the links. While those answer the question "Do closed form formulae exist for values of P(n)?", they do nto answer "What is the current research on the subject?" | |
| Oct 18, 2018 at 13:05 | review | Close votes | |||
| Oct 20, 2018 at 14:10 | |||||
| Oct 18, 2018 at 12:51 | comment | added | Gerry Myerson | See also math.stackexchange.com/questions/1029976/… | |
| Oct 18, 2018 at 12:49 | comment | added | Gerry Myerson | Possible duplicate of Convergence of the series $\sum_p p^{-s}$ ($p$ prime and $s>1$) | |
| Oct 18, 2018 at 12:36 | comment | added | Klangen | @GerryMyerson Concerning your last sentence, since ${\displaystyle \log \zeta (s)=\sum _{n>0}{\frac {P(ns)}{n}}}$, I think it is interesting enough. | |
| Oct 18, 2018 at 12:34 | history | edited | Klangen | CC BY-SA 4.0 |
edited body
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| Oct 18, 2018 at 12:34 | comment | added | Klangen | @GerryMyerson Thank you for your response. The link is already in the preamble (just click on "Math.SE") | |
| Oct 18, 2018 at 12:10 | comment | added | Gerry Myerson | I don't know what you mean by Math.SO, but whatever it may be, you should include a link here to your post there (and a link there to your post here). Anyway, I don't think anything is known about irrationality of $P(n)$. No one knows a way to get a handle on it, and no one cares too much, since $P(n)$ doesn't seem to be related to other stuff the way $\zeta(s)$ is. | |
| Oct 18, 2018 at 10:04 | comment | added | Stanley Yao Xiao | The number of proofs that we have of showing some numbers are irrational are very limited. We either show a number $\alpha$ is irrational because it is algebraic of degree greater than one (by exhibiting an irreducible polynomial $f$ of degree greater than one $f(\alpha) = 0$), or we find a sequence of rational numbers that converge to $\alpha$ way too fast (basically the idea behind the transcendence proofs of $\pi$ and $e$, and the irrationality of $\zeta(3)$). The numbers you wrote down don’t seem to be attackable by either approach, so showing that they are irrational is very hard. | |
| Oct 18, 2018 at 9:03 | history | asked | Klangen | CC BY-SA 4.0 |