Timeline for A mysterious connection between Ramanujan-type formulas for $1/\pi^k$ and hypergeometric motives
Current License: CC BY-SA 4.0
35 events
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| May 24 at 19:03 | comment | added | Jorge Zuniga | @zy I have placed new high order hypergeometric formulas for $\pi^4,\pi^{-4}$ and $\zeta(5)$ here: mathoverflow.net/questions/471939/… | |
| Apr 25 at 15:08 | comment | added | Y. Zhao | @pisco: I am very happy that you shared the proofs to the formulas...more than a suprise for me... BTW, is it possible to prove $\zeta(5)$ is irrational with the formula? | |
| Apr 25 at 14:38 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
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| Apr 25 at 14:29 | history | edited | Y. Zhao | CC BY-SA 4.0 |
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| Dec 22, 2023 at 10:17 | comment | added | pisco | Regarding formulas themselves, all of them are now proved using WZ-type method. For example your last two formulas $786/\pi^4$ and $-380928\zeta(5)$ are proved in arxiv.org/pdf/2312.14051.pdf recently. | |
| Mar 30, 2018 at 15:41 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Jan 31, 2018 at 18:44 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Jan 30, 2018 at 23:21 | comment | added | Y. Zhao | @TitoPiezasIII: I think I noticed that phenomena either. I believe Borwein brothers had searched for similar formulas(not the upside down version) extensively(but I cannot remember the name of that paper), only to re-discover those formulas discovered by Guillera and Gourevitch. | |
| Jan 30, 2018 at 14:19 | comment | added | Tito Piezas III | @zy_: You may like this post on upside down pi formulas. | |
| Jan 25, 2018 at 1:20 | comment | added | Y. Zhao | @TitoPiezasIII: I searched for hundreds of rational arguments whose numerator and denominator have small prime factors only, but I have no idea whether there is a systematic way to get all these rational arguments. Maybe an expert on arithmetic geometry will show us what the general theory behind these "identities" should be. | |
| Jan 24, 2018 at 16:42 | comment | added | Tito Piezas III | @zy_: Ah, I see it now. Yes, they are beautiful and the $\zeta(5)$ is unexpected. I noticed its argument is $-\frac{1024}{3125} = -\frac{4^5}{5^5}$ so tried to generalize it for $\zeta(7)$ using $-\frac{6^7}{7^7}$. Unfortunately, an integer relations algorithm couldn't find anything. | |
| Jan 24, 2018 at 16:25 | comment | added | Y. Zhao | @Tito Piezas: I sent an e-mail to Dr. Guillera on these discoveries. He pointed out to me that the counterpart of these three formulas has already been in his paper(formula (34)(36)(37)). He knows the upside-down version of these formulas as well. But the formulas for $1/\pi^4$,$\zeta(4)$ and $\zeta(5)$ are new to him. | |
| Jan 23, 2018 at 17:43 | comment | added | Tito Piezas III | @zy_: Are you sure those three formulas for $\zeta(3)$ are in the paper cited? I am unable to find it. | |
| S Sep 25, 2017 at 5:47 | history | bounty ended | CommunityBot | ||
| S Sep 25, 2017 at 5:47 | history | notice removed | CommunityBot | ||
| Sep 24, 2017 at 8:41 | comment | added | ypercubeᵀᴹ | Is the ! in $... = -1792\zeta(3)!$ intended or a typo? | |
| Sep 23, 2017 at 18:50 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 21, 2017 at 15:03 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 21, 2017 at 13:49 | answer | added | Will Sawin | timeline score: 12 | |
| Sep 20, 2017 at 13:39 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 19, 2017 at 19:48 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| S Sep 17, 2017 at 4:21 | history | bounty started | Y. Zhao | ||
| S Sep 17, 2017 at 4:21 | history | notice added | Y. Zhao | Canonical answer required | |
| Sep 17, 2017 at 4:20 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 14, 2017 at 21:46 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 14, 2017 at 21:33 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 14, 2017 at 16:54 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 14, 2017 at 16:45 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 14, 2017 at 1:12 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 13, 2017 at 23:18 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 13, 2017 at 22:34 | comment | added | post.as.a.guest | In the latest Magma Handbook, Watkins also tested Guillera's (96) (over ${\bf Q}(\sqrt 5)$) numerically, again finding it to seem to have a $\zeta$-factor in the $L$-function. Zudilin would be the best person to ask about the HGM connection. | |
| Sep 13, 2017 at 16:15 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 13, 2017 at 1:26 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 13, 2017 at 0:16 | history | edited | Y. Zhao | CC BY-SA 3.0 |
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| Sep 12, 2017 at 22:38 | history | asked | Y. Zhao | CC BY-SA 3.0 |