Timeline for Show that $ \lim\limits_{n\to\infty}\frac{1}{n}\sum\limits_{k=0}^{n-1}e^{ik^2}=0$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 8, 2016 at 20:52 | comment | added | Renart | Oh yeah i see it now ! nice benford's law illustration by the way. | |
| Mar 8, 2016 at 17:33 | comment | added | Sean Eberhard | Sure. It's a nice question once you see it. Actually look for a power of 2 starting 7777777..., and to get this consider the sequence $\log_{10}(2^n)$ modulo $1$. | |
| Mar 8, 2016 at 13:14 | comment | added | Renart | Thanks for the answer ! i've read a little bit of the book "uniform distribution of sequences" by L. Kuipers and H. niederreiterbut but I still don't know how to answer your question 6... Could you give me a hint/short answer ? | |
| Feb 20, 2016 at 22:31 | comment | added | Sean Eberhard | For more than you ever wanted to know about question 4, follow the links at mathoverflow.net/questions/231606/…. However, I think this question is reasonable: 4'. Show that $\{z: g_n(\alpha)\to z~\text{for some}~\alpha\} = \{z: |z|\leq 1\}$. | |
| Feb 13, 2016 at 15:48 | history | bounty ended | Renart | ||
| Feb 13, 2016 at 15:47 | vote | accept | Renart | ||
| Feb 12, 2016 at 15:35 | comment | added | Sean Eberhard | Actually not quite tangent. | |
| Feb 11, 2016 at 15:36 | comment | added | Sean Eberhard | I wrote down question 4 thinking that the answer was going to be obviously the whole unit disk or obviously just $\{0,1\}$, or something like that, but actually I think the question is rather subtle! Let $L$ be the set. Then I can prove that $L$ is a closed, convex subset of the unit disk whose boundary touches the unit circle only at $1$ and is tangent to it there. | |
| Feb 8, 2016 at 16:50 | history | answered | Sean Eberhard | CC BY-SA 3.0 |