Timeline for What might the (normalized) pair correlation function of prime numbers look like?
Current License: CC BY-SA 3.0
14 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Aug 21, 2011 at 4:41 | vote | accept | anon | ||
| Aug 20, 2011 at 8:57 | answer | added | Carlo Beenakker | timeline score: 11 | |
| Aug 18, 2011 at 12:34 | comment | added | David E Speyer | Nevermind, I was confused. Your denominator is right. | |
| Aug 18, 2011 at 3:49 | comment | added | Junkie | Lebeouf does something like this springerlink.com/content/56542774l0171258 | |
| Aug 18, 2011 at 3:13 | comment | added | Junkie | I think whatever result you get follows from the Cramer random model of the primes, or something similar as modified by Maier. Generically, one has that the density of $x$ with $\pi(x+\lambda\log x)−\pi(x)=k$ should be Poisson distributed as $e^{-\lambda}\lambda^k/k!$. This is a nearest-neighbor statistic, and if I am not wrong, the gap distribution should follow. Sorry I do not know off the top of my head or have a reference yet. | |
| Aug 18, 2011 at 3:05 | comment | added | Micah Milinovich | You may want to take a look at these lectures by Soundararajan: arxiv.org/abs/math/0606408 | |
| Aug 18, 2011 at 1:09 | comment | added | anon | @David Speyer: I'm not sure. I've added in a note at the bottom on how I got the expression, and while I believe I did the adaptation correctly, it may still be a naive substitution and in need of change. | |
| Aug 18, 2011 at 1:08 | history | edited | anon | CC BY-SA 3.0 |
added 801 characters in body
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| Aug 17, 2011 at 23:57 | comment | added | David E Speyer | That $\pi(x)$ in the denominator should be $\pi(x)^2$, right? | |
| Aug 17, 2011 at 22:37 | comment | added | David Roberts♦ | @spec - that's ok. If a question is worth cross-posting, it means it was a bad fit where it was originally posted. And there is a suitable (>2 day, say) delay to allow people to think about it. | |
| Aug 17, 2011 at 22:20 | comment | added | anon | @David Roberts: Sorry. I've seen other questions posted on both before and wasn't aware it was looked down upon. | |
| Aug 17, 2011 at 21:57 | comment | added | David Roberts♦ | Please don't post on MO and M.SE simultaneously. Among other things, it is a bad way of collecting answers in a way useful to other (esp. in the future). | |
| Aug 17, 2011 at 21:33 | history | asked | anon | CC BY-SA 3.0 |