theory of uniform distribution modulo 1

E824093

branch of number theory mathematical theory

The theory of uniform distribution modulo 1 is a branch of number theory that studies how sequences of real numbers distribute their fractional parts evenly in the unit interval.

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Observed surface forms (1)

Surface form	Occurrences
Borel’s normal number theorem	1

Statements (55)

Predicate	Object
instanceOf	branch of number theory ⓘ mathematical theory ⓘ
appliesTo	Halton sequences NERFINISHED ⓘ Sobol’ sequences NERFINISHED ⓘ multidimensional sequences in [0,1)^s ⓘ polynomial sequences (P(n)) modulo 1 ⓘ sequences (nα) modulo 1 ⓘ sequences (x_n) of real numbers ⓘ van der Corput sequences NERFINISHED ⓘ
basedOn	Birkhoff ergodic theorem NERFINISHED ⓘ Erdős–Turán inequality NERFINISHED ⓘ Koksma–Hlawka inequality NERFINISHED ⓘ Kronecker’s theorem NERFINISHED ⓘ Weyl criterion NERFINISHED ⓘ
developedBy	Harald Bohr NERFINISHED ⓘ Hermann Weyl NERFINISHED ⓘ Johannes van der Corput NERFINISHED ⓘ Mark Kac NERFINISHED ⓘ Paul Erdős NERFINISHED ⓘ
fieldOfStudy	uniform distribution modulo 1 ⓘ
hasApplicationIn	discrepancy theory NERFINISHED ⓘ numerical integration ⓘ quasi-Monte Carlo integration ⓘ randomized algorithms ⓘ
hasKeyResult	Erdős–Turán inequality for discrepancy NERFINISHED ⓘ Koksma–Hlawka inequality NERFINISHED ⓘ Kronecker’s theorem on inhomogeneous approximation NERFINISHED ⓘ Weyl criterion for uniform distribution NERFINISHED ⓘ Weyl’s theorem on polynomial sequences NERFINISHED ⓘ metric theorems on normal numbers ⓘ results on lacunary sequences ⓘ van der Corput difference theorem NERFINISHED ⓘ
relatedTo	Diophantine approximation theory NERFINISHED ⓘ ergodic theory NERFINISHED ⓘ normal numbers ⓘ probability theory NERFINISHED ⓘ pseudorandom number generation ⓘ quasi-Monte Carlo methods NERFINISHED ⓘ
studies	Diophantine approximation aspects of sequences ⓘ Kronecker sequences NERFINISHED ⓘ Weyl sums NERFINISHED ⓘ discrepancy of sequences ⓘ distribution of fractional parts of sequences ⓘ equidistribution of sequences in the unit interval ⓘ exponential sums ⓘ low-discrepancy sequences ⓘ metric distribution properties of sequences ⓘ
usesConcept	Diophantine approximation NERFINISHED ⓘ Fourier analysis NERFINISHED ⓘ discrepancy function ⓘ equidistribution ⓘ exponential functions e^{2πinx} ⓘ fractional part of a real number ⓘ measure theory ⓘ unit interval [0,1) ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Johan Frederik Koksma → contributedTo → theory of uniform distribution modulo 1 ⓘ

Émile Borel → notableWork → theory of uniform distribution modulo 1 ⓘ

this entity surface form: Borel’s normal number theorem