Timeline for Consequences of the Riemann hypothesis
Current License: CC BY-SA 4.0
25 events
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| Nov 7 at 20:30 | history | edited | KConrad | CC BY-SA 4.0 |
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| Sep 24, 2021 at 2:52 | history | edited | KConrad | CC BY-SA 4.0 |
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| Aug 17, 2021 at 3:13 | history | edited | KConrad | CC BY-SA 4.0 |
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| Feb 12, 2021 at 13:29 | comment | added | Trixie Wolf | @KConrad Thank you! "Hundreds of pages" certainly clears up why it's still in press. | |
| Feb 12, 2021 at 3:00 | history | edited | KConrad | CC BY-SA 4.0 |
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| Feb 12, 2021 at 2:46 | history | edited | KConrad | CC BY-SA 4.0 |
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| Feb 12, 2021 at 1:10 | comment | added | KConrad | @TrixieWolf: see Helfgott's reply to the question math.stackexchange.com/questions/3164020/…. | |
| Feb 12, 2021 at 0:27 | comment | added | Trixie Wolf | I don't think the 2013 Goldbach proof was accepted for publication, was it? | |
| Jul 31, 2018 at 17:14 | history | edited | José Hdz. Stgo. | CC BY-SA 4.0 |
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| S May 23, 2015 at 14:40 | history | suggested | Robin Zhang | CC BY-SA 3.0 |
remark on e) since it is now an obsolete application due to the work of Helfgott (2013)
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| May 23, 2015 at 14:18 | review | Suggested edits | |||
| S May 23, 2015 at 14:40 | |||||
| Nov 22, 2012 at 6:26 | history | edited | KConrad | CC BY-SA 3.0 |
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| Oct 24, 2010 at 2:03 | comment | added | Rob Harron | Keith, your answer is now referred to in wikipedia's Riemann hypothesis article. | |
| Aug 8, 2010 at 7:07 | comment | added | Simon Pepin Lehalleur | Very nice ! But a very nice consequence of GRH is missing : the result of Shoup which says that the least primitive root mod p is $O(log(p)^6)$ (he also proved an analogue for $\mathbb{F}_{p^2}). | |
| Mar 7, 2010 at 17:16 | comment | added | Victor Miller | As for (h) (Artin's Primitive root conjecture), anyone interested should read Pieter Moree's excellent survey arxiv.org/pdf/math/0412262 . One thing that should be mentioned here is Bombieri's mean value theorem, which basically says that the GRH for a bunch of L-functions is true "on the average" -- one way of saying that is that if one assumes the good remainders that one would get from assuming the GRH (say) for the set of L-function of Dirichlet character mod q, in some interval, you can get unconditional consequences that would be obtained by the adding the GRH remainders. | |
| Mar 6, 2010 at 2:14 | comment | added | Felipe Voloch | f) is still relevant even after AKS. The same ideas give (under GRH) polynomial time deterministic algorithms to construct a primitive root and a quadratic non-residue mod p. Without GRH we don't know how to do these. | |
| Mar 6, 2010 at 1:54 | vote | accept | Andrea Ferretti | ||
| Mar 6, 2010 at 1:08 | comment | added | Andrea Ferretti | I'm now sorry I made the question community wiki. I think your answer is very interesting and surely involved a lot of work, and should deserve points | |
| Mar 6, 2010 at 0:51 | history | edited | KConrad | CC BY-SA 2.5 |
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| Mar 6, 2010 at 0:12 | history | edited | KConrad | CC BY-SA 2.5 |
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| Mar 5, 2010 at 23:57 | history | edited | KConrad | CC BY-SA 2.5 |
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| Mar 5, 2010 at 23:14 | comment | added | Qiaochu Yuan | Regarding i), this doesn't seem to be the strongest expected result. If we had O(n^{1+e}) for every e, then there would exist groups of size O(n^{2+e}) with n-dimensional irreducible representations for every n: see mathoverflow.net/questions/530/… . | |
| Mar 5, 2010 at 23:06 | history | edited | KConrad | CC BY-SA 2.5 |
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| Mar 5, 2010 at 22:55 | history | edited | KConrad | CC BY-SA 2.5 |
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| Mar 5, 2010 at 22:17 | history | answered | KConrad | CC BY-SA 2.5 |