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New posts in equidistribution
Why does a golden angle based spiral produce evenly distributed points?
fibonacci-numbers
golden-ratio
equidistribution
show that $ \limsup n\; | \;\{ (n+1)^2 \sqrt{2}\} - \{ n^2 \sqrt{2}\}\; | = \infty $
sequences-and-series
number-theory
alternative-proof
divergent-series
equidistribution
Uniformly distributed rationals
real-analysis
analysis
equidistribution
Applications of equidistribution
sequences-and-series
equidistribution
$(n^2 \alpha \bmod 1)$ is equidistributed in $\mathbb{T}^2$ if $\alpha \in \mathbb{R} \setminus \mathbb{Q}$
functional-analysis
ergodic-theory
equidistribution
When is a sequence $(x_n) \subset [0,1]$ dense in $[0,1]$?
general-topology
sequences-and-series
diophantine-approximation
equidistribution
Are the fractional parts of $\log \log n!$ equidistributed or dense in $[0,1]$?
number-theory
reference-request
dynamical-systems
equidistribution
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
real-analysis
fourier-analysis
ergodic-theory
equidistribution
What is wrong with the following proof that $\{ (\frac{3}{2})^n\mod 1: n\in\mathbb{N} \} $ is dense in $\ [0,1]\ $?
solution-verification
open-problem
equidistribution
Prove that $\lim_{N\rightarrow\infty}(1/N)\sum_{n=1}^N f(nx)=\int_{0}^1f(t)dt$
real-analysis
analysis
equidistribution
An equidistributed sequence: $an^\sigma$ for $a\neq0$ and $\sigma$ noninteger
calculus
real-analysis
asymptotics
ergodic-theory
equidistribution
Equidistribution of $an^\sigma$ for $\sigma\in(0,1)$
fourier-analysis
equidistribution
Show that $ \lim\limits_{n\to\infty}\frac{1}{n}\sum\limits_{k=0}^{n-1}e^{ik^2}=0$
real-analysis
limits
exponential-sum
equidistribution
Is the Fibonacci lattice the very best way to evenly distribute N points on a sphere? So far it seems that it is the best?
fibonacci-numbers
lattice-orders
golden-ratio
spheres
equidistribution
$\sin (n^2)$ diverges
limits
trigonometry
convergence-divergence
equidistribution
A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
sequences-and-series
equidistribution
summation-by-parts
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