Timeline for Partial sums of multiplicative functions
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jan 13, 2010 at 19:51 | history | edited | Mark Lewko | CC BY-SA 2.5 |
added 14 characters in body
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| Jan 13, 2010 at 16:57 | comment | added | Idoneal | It should be $\sqrt{Q}\log \log Q$ in the above comment. The sums are trivially bounded by $Q$ and it is not too hard to show that the inequality (Polya-Vinogradov) $\sum_{M\leq n \leq M+N} \chi(n) = O(\sqrt{Q} \log Q)$ holds no matter how large $N$ is. @Pete: they are quite similar from the point of view of L-functions. The key word here is "conductor", which puts "t" and "q" in the same footing. See the beginning of chapter 5 of the book by Iwaniec-Kowalski for detail. | |
| Jan 9, 2010 at 12:16 | comment | added | Pete L. Clark | Since Dirichlet characters are periodic, their partial sums are uniformly bounded. Thus one seeks bounds for families of Dirichlet characters in terms of the modulus, which seems rather different from the situation of $\mu$ and $\lambda$. (Disclaimer: I am not an analytic number theorist. Maybe there's more of a similarity here than is immediately apparent.) | |
| Jan 9, 2010 at 2:19 | history | answered | Mark Lewko | CC BY-SA 2.5 |