In mathematics, the equidistribution theorem is the statement that the sequence a, 2a, 3a, ... mod 1 is uniformly distributed on the circle R / Z {\displaystyle...

or by an − ⌊an⌋, is equidistributed in the interval [0, 1]. The equidistribution theorem: The sequence of all multiples of an irrational α, 0, α, 2α, 3α...

differential equations on a smooth manifold.) The equidistribution theorem is a special case of the ergodic theorem, dealing specifically with the distribution...

typical set used in theories of data compression. Roughly speaking, the theorem states that although there are many series of results that may be produced...

the distribution is uniform by the equidistribution theorem. Weyl's criterion Dirichlet's approximation theorem Kronecker, L. (1884), "Näherungsweise...

Dirichlet's unit theorem (algebraic number theory) Equidistribution theorem (ergodic theory) Erdős–Kac theorem (number theory) Euclid's theorem (number theory)...

other two. Equidistribution theorem Lonely runner conjecture Allouche, Jean-Paul; Shallit, Jeffrey (2003), "2.6 The Three-Distance Theorem", Automatic...

In mathematics, a Weyl sequence is a sequence from the equidistribution theorem proven by Hermann Weyl: The sequence of all multiples of an irrational...

angle measure dθ/2π on the unit circle, and T a rotation. See equidistribution theorem; the Bernoulli scheme; the interval exchange transformation; with...

K. (2007), "Sieving and the Erdős-Kac theorem", in Granville, Andrew; Rudnick, Zeév (eds.), Equidistribution in number theory, an introduction: Proceedings...

Zeév (eds.), Equidistribution in number theory, an introduction. Proceedings of the NATO Advanced Study Institute on equidistribution in number theory...

Ratner equidistribution theorem further asserts that each such orbit is equidistributed in its closure. The Ratner measure classification theorem is the...

theory it is applied in the discrete uniform distribution and the equidistribution theorem for rational numbers. If there are n {\textstyle n} events under...

formula Wiener–Khinchin theorem Khinchin inequality Equidistribution theorem Khinchin's constant Khinchin–Lévy constant Khinchin's theorem on Diophantine approximations...

Birkhoff–Kellogg invariant-direction theorem Poincaré–Birkhoff theorem Equidistribution theorem Chromatic polynomial Recurrent point Topological dynamics Morse...

irrational number. This is a straightforward consequence of the equidistribution theorem. Raimi, Ralph A. (August–September 1976). "The first digit problem"...

logarithmic, in relation with the Riemann zeta function. See also equidistribution theorem. Let p be an odd prime and let ξ = e 2 π i / p {\displaystyle \xi...

semisimple groups and semisimple Lie algebras Weyl's theorem on eigenvalues Weyl's criterion for equidistribution (Weyl's criterion) Weyl's lemma on the hypoellipticity...

counter modulo 232 (which he calls a "Weyl sequence" after Weyl's equidistribution theorem). This also increases the period by a factor of 232, to 2192−232:...

2,3,\ldots \}} is equidistributed mod 2π, a consequence of the equidistribution theorem.) An example from number theory is lim inf n → ∞ ( p n + 1 − p...

{\displaystyle T_{\pi ,\lambda }} is just a circle rotation. The Weyl equidistribution theorem then asserts that if the length λ 1 {\displaystyle \lambda _{1}}...

Compositio Mathematica, 104 (1): 77–105. Zhang, Shou-Wu (1998), "Equidistribution of small points on abelian varieties", Annals of Mathematics, 147 (1):...

publications of the Plancherel theorem and Carathéodory's theorem, Hermann Weyl's proof of the equidistribution theorem, and one of the appendices to Henri...

(e.g. quantum ergodicity, equidistribution of eigenfunctions in billiard geometries, quantum ergodic restriction theorems to separating hypersurfaces)...

manifolds" (2018), Annals of Mathematics Joint with Marques and Neves: "Equidistribution of minimal hypersurfaces for generic metrics" (2019), Inventiones mathematicae...

of a set drawn from harmonic analysis, and the Van der Corput theorem on equidistribution modulo 1. He became member of the Royal Netherlands Academy of...

Eskin, Alex; Mirzakhani, Maryam; Mohammadi, Amir (2015). "Isolation, equidistribution, and orbit closures for the SL(2,R) action on moduli space". Annals...

Studies, Princeton 2005, ISBN 0691123306. Convolution and equidistribution: Sato-Tate theorems for finite-field Mellin transforms. Annals of Mathematical...

ISBN 978-0-521-24383-4. Granville, Andrew; Rudnick, Zeev (7 January 2007). Equidistribution in Number Theory, An Introduction. Nato Science Series II. Vol. 237...

and complex power sums. The method has been applied to problems in equidistribution. The method applies to sums of the form s ν = ∑ n = 1 N b n z n ν  ...