Timeline for Where does the error term of the Prime Number Theorem touch the predicted asymptotic behavior
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 20, 2011 at 15:20 | comment | added | GH from MO | @Micah: Thanks for the valuable comment. | |
| Jul 20, 2011 at 14:43 | comment | added | Micah Milinovich | @Mark: Thanks for the paper! @GH: Gonek has a conjecture for the summatory function of the Moebius function which is analogous to Montgomery's conjecture for the error term in PNT. The details are in Nathan Ng's paper "The distribution of the summatory function of the Moebius function" which he has posted on his web-page. | |
| Jul 20, 2011 at 2:12 | comment | added | Mark Lewko | @GH, I temporarily put a copy up at: lewko.files.wordpress.com/2011/07/… the relevant section starts on page 14. | |
| Jul 20, 2011 at 1:19 | comment | added | GH from MO | Dear Mark, thank you. Is this paper available online? | |
| Jul 20, 2011 at 0:09 | comment | added | Mark Lewko | Montgomery's conjecture is discussed in his paper "The zeta function and prime numbers," Proceedings of the Queen's Number Theory Conference, 1979, Queen's Univ., Kingston, Ont., 1980, 1-31. He calculates, assuming RH and the zeros of the zeta function are linearly independent, the limiting distribution of the quantity $e^{-y/2}(\psi(e^y)-e^y)$. Once one knows this distribution it is natural to conjecture how large $|e^{-y/2}(\psi(e^y)-e^y)|$ can be (infinity often) on probabilistic grounds. | |
| Jul 19, 2011 at 21:41 | comment | added | François G. Dorais | I thought the quote was "$\log\log\log x$ goes to infinity with great dignity." | |
| Jul 19, 2011 at 21:02 | comment | added | Victor Miller | It reminds me of the quote "$\log \log x$ approaches infinity but has never been observed to do so." | |
| Jul 19, 2011 at 20:56 | comment | added | David Hansen | (And it's hard (impossible?) to spot $\log{\log{\log{}}}$ "in nature".) | |
| Jul 19, 2011 at 20:21 | history | answered | GH from MO | CC BY-SA 3.0 |