Timeline for Double sum of reciprocal powers of integer LCMs
Current License: CC BY-SA 2.5
4 events
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| Aug 1, 2010 at 3:42 | comment | added | serdar | Brad, Thanks for the pointers and for clarifying the proof. Unfortunately, I do not know how to respond directly with a comment, hence my comment ended up being an answer. | |
| Jul 31, 2010 at 1:36 | comment | added | Brad Rodgers | Two other observations: 1) Aurel Wintner's paper "Diophantine Approximations and Hilbert's Space" may be relevant to what you're looking for. 2) Usually on math overflow it is best to respond by adding a comment rather than another answer. I did the same thing when I joined, so no real worries though. In a lot of ways I think a discussion board format is much more natural than the format here... | |
| Jul 31, 2010 at 1:31 | comment | added | Brad Rodgers | I can't find it in Polya and Szego either, so I must be thinking of another book! At any rate, I saw it for the first time when a friend showed it to me. Given that for fixed $k$, $S(n,k) \sim \zeta(k)^3/\zeta(2k)$, the best we can hope for in bounding $S(n,k)$ is (unfortunately perhaps) $O(n^k).$ If $n$ and $k$ tend to infinity in concert (e.g. $n=k$) then one could get a better bound, but it would depend upon how $n$ and $k$ tend to infinity together (and might be a very messy bound at that). Anyway, since I couldn't find the reference, I'm editing the post above to contain the proof... | |
| Jul 29, 2010 at 12:22 | history | answered | serdar | CC BY-SA 2.5 |