Question

Equidistributed Sequences and Riemann-Integrability

score 46 · Answer 1 · 2023-05-15 15:28:49

46

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Equidistributed Sequences and Riemann-Integrability

Published on 15 May 2023 - 15:28

score 54 · Answer 2 · 2023-06-07 09:40:08

54

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If $x > 1$ then does the set $ \lbrace{ \lbrace{ x^n\rbrace}: n\in\mathbb{N} \rbrace}\ $ always contain either $0$ or $1$ as a limit point?

Published on 07 Jun 2023 - 9:40

score 168 · Answer 3 · 2023-08-29 13:09:52

168

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How does this algorithm for the Van der Corput sequence work?

Published on 29 Aug 2023 - 13:09

score 47 · Answer 4 · 2023-09-09 20:33:06

47

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When is the convolution of two sequences equidistributed?

Published on 09 Sep 2023 - 20:33

score 70 · Answer 5 · 2023-09-13 13:36:39

70

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Probability that the first $m$ digits in $2^n$ are $k_1k_2\dots k_m$

Published on 13 Sep 2023 - 13:36

score 142 · Answer 6 · 2023-10-03 11:00:14

142

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General proposition that, if true, would immediately prove that $\sum\sin n$ and $\sum\cos n$ are bounded

Published on 03 Oct 2023 - 11:00

score 134 · Answer 7 · 2023-11-05 14:18:26

134

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Let $(a_{n})_{n\in N}=(1,2,3,4,6,8,9,12,\cdots)$ list the set$\{2^n3^m\mid m,n\in N\}$. Find α such that $(a_n)\alpha\pmod1$ is not equidistributed.

Published on 05 Nov 2023 - 14:18

score 21 · Answer 8 · 2023-11-08 00:43:18

21

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$(\Delta^{(\infty)})^{p+1} \leq N(p+1)\Delta^{(p)}$ i.e. Equivalence of $p$-discrepancies

Published on 08 Nov 2023 - 0:43

score 39 · Answer 9 · 2023-11-08 16:12:04

39

Views

Question regarding behaviour of equidistributed sequences.

Published on 08 Nov 2023 - 16:12

score 59 · Answer 10 · 2024-01-09 17:10:33

59

Views

Questions regarding the function $\Omega(n)$

Published on 09 Jan 2024 - 17:10

score 157 · Answer 11 · 2024-01-12 05:59:12

157

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Intuition behind Weyl's equidistribution theorem

Published on 12 Jan 2024 - 5:59

score 20 · Answer 12 · 2024-01-15 00:57:53

20

Views

Stuck on proof equidistribution on homogeneous space

Published on 15 Jan 2024 - 0:57

score 311 · Answer 13 · 2024-01-15 22:42:52

311

Views

For each $n\in\mathbb{N},$ let $x_n:=\min_{1\leq k < n}\lvert\sin n-\sin k\rvert.\ $ Does $\sum_{n=1}^{\infty} x_n $ converge?

Published on 15 Jan 2024 - 22:42

score 54 · Answer 14 · 2024-03-13 19:15:36

54

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Is $\{n\log n \pmod 1: n\in\mathbb{N} \}$ dense in $[0,1]?$ If so, is it uniformly distributed?

Published on 13 Mar 2024 - 19:15

score 37 · Answer 15 · 2015-01-29 19:08:42

37

Views

Is there always a g in a compact connected Lie group whose powers equidistributes in G?

Published on 29 Jan 2015 - 19:08

List Question

Equidistributed Sequences and Riemann-Integrability

If $x > 1$ then does the set $ \lbrace{ \lbrace{ x^n\rbrace}: n\in\mathbb{N} \rbrace}\ $ always contain either $0$ or $1$ as a limit point?

How does this algorithm for the Van der Corput sequence work?

When is the convolution of two sequences equidistributed?

Probability that the first $m$ digits in $2^n$ are $k_1k_2\dots k_m$

General proposition that, if true, would immediately prove that $\sum\sin n$ and $\sum\cos n$ are bounded

Let $(a_{n})_{n\in N}=(1,2,3,4,6,8,9,12,\cdots)$ list the set$\{2^n3^m\mid m,n\in N\}$. Find α such that $(a_n)\alpha\pmod1$ is not equidistributed.

$(\Delta^{(\infty)})^{p+1} \leq N(p+1)\Delta^{(p)}$ i.e. Equivalence of $p$-discrepancies

Question regarding behaviour of equidistributed sequences.

Questions regarding the function $\Omega(n)$

Intuition behind Weyl's equidistribution theorem

Stuck on proof equidistribution on homogeneous space

For each $n\in\mathbb{N},$ let $x_n:=\min_{1\leq k < n}\lvert\sin n-\sin k\rvert.\ $ Does $\sum_{n=1}^{\infty} x_n $ converge?

Is $\{n\log n \pmod 1: n\in\mathbb{N} \}$ dense in $[0,1]?$ If so, is it uniformly distributed?

Is there always a g in a compact connected Lie group whose powers equidistributes in G?

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