Timeline for Positive upper asymptotic density and equidistribution
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 30, 2018 at 9:50 | comment | added | Fedor Petrov | @Jean you mean equidistributed modulo 1? Of course no, take $x_n=n\sqrt{2}, y_n=[x_n]$. | |
| Mar 30, 2018 at 9:03 | comment | added | Jean | @GregMartin I mean $x_n/y_n\to 1$ as $n\to \infty$. | |
| Mar 30, 2018 at 1:45 | comment | added | Greg Martin | If by "asymptotic equivalent" you mean that $x_n-y_n$ tends to $0$ as $n\to\infty$, then yes, it is an easy consequence of the definition of equidistribution that $\{x_n\}$ is equidistributed if and only if $\{y_n\}$ is. | |
| Mar 29, 2018 at 22:22 | comment | added | Jean | Thanks, I didn't see that. But for example, if I have two asymptotic equivalent sequences $x_n$ and $y_n$. If $x_n$ is equidistributed then so $y_n$? | |
| Mar 29, 2018 at 21:13 | history | answered | Fedor Petrov | CC BY-SA 3.0 |