Timeline for Rational approximations on the circle
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2013 at 7:07 | review | Suggested edits | |||
| Aug 23, 2013 at 7:18 | |||||
| Aug 12, 2013 at 5:21 | review | Suggested edits | |||
| Aug 12, 2013 at 5:29 | |||||
| Apr 19, 2011 at 19:40 | comment | added | GH from MO | @Sergei: Unfortunately I don't know, so I was not completely right saying "the answer is affirmative". The state of the art seems to be set by Matveev (MR1817252) improving on the previous strong result by Baker-Wüstholz (MR1234835). The latter is available online: digizeitschriften.de/dms/img/… I would probably ask the authors of these papers how significant is the dependence on the heights. Probably this dependence is substantial even for $\alpha$ on the unit circle, but I am no expert. | |
| Apr 19, 2011 at 18:32 | comment | added | Sergei Ivanov | Thanks, I think I got it now. Do you know if the exponent can be bounded in terms of degree of $\alpha$ (not involving height or whatever)? | |
| Apr 19, 2011 at 17:11 | comment | added | GH from MO | @Sergei: In the second theorem cited on the MR page, $m=2$, $H_0=q$, while $h$ and $n$ are positive constants depending on $\alpha$, so the bound is of the form $>\exp(-c_1-c_2*\ln q)=c_3 q^{-c_2}$ with constants $c_i>0$ depending on $\alpha$. | |
| Apr 19, 2011 at 16:42 | comment | added | Sergei Ivanov | Can you elaborate on how to apply Feldman's result here? I could only get something like $C(\alpha)/q^{\log q}$ from the first theorem cited on the MR page, and an estimate exponential in $q$ from the second one. | |
| Apr 19, 2011 at 15:15 | history | answered | GH from MO | CC BY-SA 3.0 |