Timeline for Partial sums of multiplicative functions
Current License: CC BY-SA 3.0
15 events
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| Sep 20, 2017 at 11:59 | comment | added | Robert Frost | I had an idea that it might be worth a) defining exhaustively the algebra of functions which are multiplicative on the domain of positive integers and b) the modular form of the same algebra based on any two elements being considered equivalent if they yield the same Euler product, which although an ambitious enterprise should surely yield some new insight into this area. math.stackexchange.com/questions/2436382 | |
| Nov 4, 2014 at 20:24 | history | edited | GH from MO | CC BY-SA 3.0 |
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| S Sep 20, 2014 at 4:01 | history | suggested | Mayank Pandey | CC BY-SA 3.0 |
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| Sep 20, 2014 at 3:38 | review | Suggested edits | |||
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| Aug 6, 2012 at 21:52 | comment | added | Frank Thorne | Greg -- indeed, that's what I meant, thank you! | |
| Aug 30, 2011 at 4:52 | comment | added | Greg Martin | Frank, you must mean a constant times $x (\log x)^{a-1}$. One reference is my paper with Finch and Sebah (Google knows it), although the best use of that hint is to find more primary references from my paper's bibliography. | |
| Jun 29, 2011 at 3:34 | comment | added | Frank Thorne | I heard from Andrew Granville that the following is (roughly) true: Let $f(n)$ be a completely multiplicative function, with |f(n)| = 1, such that the mean value of $f(p)$ is equal to $\alpha \neq 0, -1$. Then under some technical conditions, $\sum_{n < x} f(n)$ is asymptotic to a constant times $(\log x)^{\alpha - 1}$. Apparently this is due to Tenenbaum, based on ideas of Selberg. Unfortunately I'm not familiar with the proof, nor do I know a reference. | |
| Feb 5, 2010 at 5:08 | answer | added | Peter Humphries | timeline score: 8 | |
| Jan 15, 2010 at 10:33 | history | edited | gowers |
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| Jan 13, 2010 at 20:00 | history | edited | Michael Lugo |
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| Jan 9, 2010 at 2:19 | answer | added | Mark Lewko | timeline score: 2 | |
| Jan 8, 2010 at 19:43 | answer | added | mnf | timeline score: 4 | |
| Jan 8, 2010 at 8:34 | answer | added | engelbrekt | timeline score: 16 | |
| Jan 7, 2010 at 23:23 | answer | added | David E Speyer | timeline score: 15 | |
| Jan 7, 2010 at 23:16 | history | asked | gowers | CC BY-SA 2.5 |