Timeline for Roth's Theorem Variations?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 7, 2023 at 12:34 | comment | added | David E Speyer | Agreed, I don't see a reduction in other direction. | |
| Dec 7, 2023 at 6:49 | comment | added | David Feldman | @DavidESpeyer Well that was indeed what I was thinking about. But only "similar" right? My conjecture could be false without scuttling normality, right? I mean that the infinitely many "long strings of zeroes" could arise so rarely that they would not spoil the statistics. So the two questions are mutually independent for all we know. | |
| Dec 7, 2023 at 2:04 | comment | added | David E Speyer | Such a bound is basically the same as asking that the decimal expansion of $x$ not have any long strings of zeroes too early, and is similar to the question of whether $x$ is normal en.wikipedia.org/wiki/Normal_number . Almost nothing is known about proving concrete numbers are normal, so I would suspect nothing like this is known. See mathoverflow.net/questions/23547 for similar discussion. | |
| Dec 6, 2023 at 23:05 | comment | added | David Feldman | @StanleyYaoXiao I think you want $\kappa > 1$ and then that's Lang's conjectures, but my question is in a different direction, because I'm not asking about all rational approximators. | |
| Dec 6, 2023 at 23:05 | comment | added | David Feldman | @mathworker21 Yes. | |
| Dec 6, 2023 at 21:14 | comment | added | Stanley Yao Xiao | Roth's theorem is famously ineffective, so attempting to improve the denominator from $q^{2 + \varepsilon}$ to something like $q^2 (\log q)^\kappa$ for some $\kappa > 0$ would be extremely difficult. | |
| Dec 6, 2023 at 21:02 | comment | added | mathworker21 | is your question (at the end) just about irrational real algebraic numbers? | |
| Dec 6, 2023 at 20:59 | history | asked | David Feldman | CC BY-SA 4.0 |