Timeline for sums of fractional parts of linear functions of n
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 12, 2013 at 3:49 | review | Suggested edits | |||
| Dec 12, 2013 at 9:49 | |||||
| Feb 18, 2011 at 21:58 | vote | accept | James Propp | ||
| Feb 11, 2011 at 15:11 | answer | added | David E Speyer | timeline score: 5 | |
| Feb 11, 2011 at 12:31 | answer | added | Sinai Robins | timeline score: 3 | |
| Feb 9, 2011 at 4:43 | comment | added | Gerry Myerson | David, I've posted a solution, so 1) the question is not all that difficult, or 2) my solution is wrong, or 3) I've settled the Riemann Hypothesis. RH, I think, is equivalent to sharp estimates of Farey discrepancy, but less-than-sharp estimates are not so hard to come by, and can still be useful. | |
| Feb 8, 2011 at 23:22 | comment | added | David Feldman | This might be a very difficult question. $C_m(\alpha,0)$ is continuous, indeed linear with constant slope, except for discontinuities located on a Farey sequence. So the order of magnitude you ask for might be related to the discrepancy of Farey sequences, and versions of that question turn out equivalent to RH. It's not hard to express $C_m(\alpha,0)$ as a Fourier series, but the Fourier coefficients have number theoretic content. | |
| Feb 8, 2011 at 7:07 | comment | added | David Feldman | I'm confused by "I'd settle for an answer in the case where $\gamma = 0$ ." That doesn't sound like a "case," but a different (and not obviously easier) question. | |
| Feb 8, 2011 at 6:23 | answer | added | Gerry Myerson | timeline score: 10 | |
| Feb 8, 2011 at 5:19 | history | asked | James Propp | CC BY-SA 2.5 |