Question

How to describe following set $\{ 1 \leq n \leq N: \alpha_n \in]a,b[\}$?

score 140 · Answer 1 · 2012-10-29 16:46:07

140

Views

How to describe following set $\{ 1 \leq n \leq N: \alpha_n \in]a,b[\}$?

Published on 29 Oct 2012 - 16:46

score 665 · Answer 2 · 2020-08-04 19:03:52

665

Views

${α⋅ \log(n)}$ is not uniformly distributed mod1 in $[0,1]$

Published on 04 Aug 2020 - 19:03

score 236 · Answer 3 · 2020-09-20 13:29:32

236

Views

Equidistribution theorem in two dimension

Published on 20 Sep 2020 - 13:29

score 302 · Answer 4 · 2020-10-12 04:25:44

302

Views

Fractional part of a log n is not equidistributed

Published on 12 Oct 2020 - 4:25

score 44 · Answer 5 · 2021-01-17 17:02:22

44

Views

Effective equidistribution for number with bounded irrationality measure

Published on 17 Jan 2021 - 17:02

score 353 · Answer 6 · 2021-03-02 15:03:26

353

Views

Uniform distribution of points on a sphere

Published on 02 Mar 2021 - 15:03

score 108 · Answer 7 · 2021-03-04 03:02:34

108

Views

Something similar to Kronecker's Theorem

Published on 04 Mar 2021 - 3:02

score 42 · Answer 8 · 2021-11-27 04:46:43

42

Views

Ratner's theorem on equidistribution for abelian linear sequences

Published on 27 Nov 2021 - 4:46

score 26 · Answer 9 · 2021-11-27 06:16:18

26

Views

Understanding the Single-scale equidistribution theorem for abelian polynomial sequences using example

Published on 27 Nov 2021 - 6:16

score 28 · Answer 10 · 2021-12-16 14:52:36

28

Views

Does equidistribution of $(a_n)_{n\in\mathbb{N}}$ imply equidistribution of $(a_n+a_{n+k})_{n\in\mathbb{N}}$?

Published on 16 Dec 2021 - 14:52

score 247 · Answer 11 · 2021-12-26 17:28:40

247

Views

What is wrong with the following proof that $\{ (\frac{3}{2})^n\mod 1: n\in\mathbb{N} \} $ is dense in $\ [0,1]\ $?

Published on 26 Dec 2021 - 17:28

score 288 · Answer 12 · 2021-12-26 20:16:58

288

Views

Show that $\lim_{N\to\infty}\int_0^1 \left|\frac1N\sum_{n=1}^N f(x+\xi_n) \right|^{\,2}\, dx = 0$ if $\int_0^1 f(x)\, dx = 0$ and $f$ is periodic

Published on 26 Dec 2021 - 20:16

score 77 · Answer 13 · 2022-01-13 00:47:36

77

Views

Equidistribution of Polynomials with At Least One Irrational Coeﬃcients

Published on 13 Jan 2022 - 0:47

score 65 · Answer 14 · 2022-03-08 18:55:46

65

Views

Inequality for sum of sines over integers in $[1;x]$

Published on 08 Mar 2022 - 18:55

score 18 · Answer 15 · 2026-03-17 13:41:53

18

Views

How do we show such set is equidistributed when it is involved from the image of local set?

Published on 17 Mar 2026 - 13:41

List Question

How to describe following set $\{ 1 \leq n \leq N: \alpha_n \in]a,b[\}$?

${α⋅ \log(n)}$ is not uniformly distributed mod1 in $[0,1]$

Equidistribution theorem in two dimension

Fractional part of a log n is not equidistributed

Effective equidistribution for number with bounded irrationality measure

Uniform distribution of points on a sphere

Something similar to Kronecker's Theorem

Ratner's theorem on equidistribution for abelian linear sequences

Understanding the Single-scale equidistribution theorem for abelian polynomial sequences using example

Does equidistribution of $(a_n)_{n\in\mathbb{N}}$ imply equidistribution of $(a_n+a_{n+k})_{n\in\mathbb{N}}$?

What is wrong with the following proof that $\{ (\frac{3}{2})^n\mod 1: n\in\mathbb{N} \} $ is dense in $\ [0,1]\ $?

Show that $\lim_{N\to\infty}\int_0^1 \left|\frac1N\sum_{n=1}^N f(x+\xi_n) \right|^{\,2}\, dx = 0$ if $\int_0^1 f(x)\, dx = 0$ and $f$ is periodic

Equidistribution of Polynomials with At Least One Irrational Coeﬃcients

Inequality for sum of sines over integers in $[1;x]$

How do we show such set is equidistributed when it is involved from the image of local set?

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