Timeline for Is $\zeta(3)/\pi^3$ rational?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| S May 8 at 5:02 | history | suggested | Ukhukanya | CC BY-SA 4.0 |
The Apery paper was in 1979
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| May 8 at 3:23 | review | Suggested edits | |||
| S May 8 at 5:02 | |||||
| Sep 1, 2019 at 18:51 | comment | added | Lucian | Intuitively speaking, all $\zeta(2n)$ are sums of squares, as is also the algebraic equation of the circle, $x^2+y^2=r^2,~$ whose constant $\pi$ is. | |
| Feb 8, 2017 at 1:53 | comment | added | Gerry Myerson | Question also arose at m.se, math.stackexchange.com/questions/35412/… | |
| Aug 18, 2016 at 5:16 | comment | added | Jonas Meyer | @NoamD.Elkies: I was unclear. "this" meant the one asked here, not the one referred to previously in that sentence. | |
| Aug 18, 2016 at 1:24 | comment | added | Noam D. Elkies | @JonasMeyer "$\zeta(3)$ is algebraically independent of $\pi$" is a much stronger conjecture than $\zeta(3)$ is not a rational multiple of $\pi^3$, so naturally the algebraic independence is not known either. | |
| Aug 18, 2016 at 0:54 | comment | added | Per Alexandersson | Perhaps one can ask if $\zeta(3)^a/\zeta(5)^b$ is rational for some pair of positive integers $(a,b)$... | |
| S Aug 18, 2016 at 0:22 | history | suggested | CommunityBot | CC BY-SA 3.0 |
fixed mathjax formatting
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| Aug 18, 2016 at 0:12 | review | Suggested edits | |||
| S Aug 18, 2016 at 0:22 | |||||
| May 9, 2011 at 21:40 | answer | added | AFK | timeline score: 6 | |
| May 9, 2011 at 20:58 | answer | added | DamienC | timeline score: 21 | |
| May 9, 2011 at 14:35 | answer | added | user02138 | timeline score: 15 | |
| Apr 5, 2011 at 0:20 | answer | added | Gerry Myerson | timeline score: 27 | |
| Apr 4, 2011 at 21:38 | comment | added | Ramsey | Just to expand on Kevin's answer in a way that might help you to do some relevant searches: the positive even integers and negative odd integers are "critical integers" for the motive of which $\zeta(s)$ is the associated motivic $L$-function (namely, $Spec(\mathbb{Q})$). These are the ones to which a conjecture of Deligne applies that "explains" why $\zeta(k)\pi^{-k}\in \mathbb{Q}$ for positive even $k$. | |
| Apr 4, 2011 at 21:11 | answer | added | Gerald Edgar | timeline score: 7 | |
| Apr 4, 2011 at 20:15 | comment | added | Kevin Buzzard | It's actually not natural to ask whether $\zeta(3)$ is a rational multiple of $\pi^3$! There are "natural" conjectures to make about special values of a huge class of zeta functions, including Riemann's, and once you have figured out what's going on then you realise that the (conjectural) story for Riemanns zeta should be quite different at odd and even integers. Evidence for this: look at the values of Riemann's zeta at negative integers! it always vanishes at $-2,-4,-6,\ldots$ and never vanishes at $-1,-3,-5,\ldots$. | |
| Apr 4, 2011 at 19:43 | comment | added | Faisal | Also relevant: mathoverflow.net/questions/38190/… | |
| Apr 4, 2011 at 19:39 | comment | added | Jonas Meyer | You may find mathoverflow.net/questions/30659/… useful, with a relevant comment by Wadim Zudilin and answer by Emerton. It is conjectured algebraically independent of $\pi$, but it doesn't seem that even this weaker result is known. | |
| Apr 4, 2011 at 19:27 | history | asked | Thomas Bloom | CC BY-SA 2.5 |