Timeline for How often does the Mertens function vanish?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 22, 2019 at 11:09 | history | bounty ended | Basj | ||
| Jan 15, 2019 at 17:13 | comment | added | Greg Martin | Teaching you to fish: :) Typing "Fiorilli" into The Mathematics Genealogy Project uncovers the title of his thesis, Irrégularités dans la distribution des nombres premiers et des suites plus générales dans les progressions arithmétiques; the first Google hit gets you the PDF. It definitely uses complex methods, specifically the explicit formula. | |
| Jan 15, 2019 at 11:16 | comment | added | Basj | @kodlu Interesting article, that uses complex analysis techniques. Do you know if there are elementary techniques that can prove the same thing? | |
| Jan 11, 2019 at 0:11 | vote | accept | Basj | ||
| Jan 10, 2019 at 11:28 | comment | added | kodlu | @Basj, how can I get the PDF to you? I don't have a webpage I can upload to. | |
| Jan 9, 2019 at 21:24 | comment | added | kodlu | @SylvainJULIEN, yes. Basj, I will see if I can track down a PDF. | |
| Jan 9, 2019 at 18:12 | comment | added | Greg Martin | To the best of my knowledge, nothing stronger than $\Omega(\log y)$ is known for the number of sign changes of any of the usual number-theoretic functions and their error terms. Even showing that the number of sign changes grows faster than any constant multiple of $\log y$ seems quite difficult. Daniel Fiorilli pointed out in his thesis that one of the reasons we can't do better (despite the truth probably being around $\sqrt y$) is that these proofs use a many-times-averaged version of these functions, which actually do have only $O(\log y)$ sign changes. | |
| Jan 9, 2019 at 17:49 | comment | added | Sylvain JULIEN | I guess c is the imaginary part of the first non trivial zero of zeta ? | |
| Jan 9, 2019 at 16:18 | history | answered | kodlu | CC BY-SA 4.0 |