Berry-Esseen bounds and a theorem of Erdős and Turan on uniform distribution mod 1

DOI10.1215/S0012-7094-73-04055-6zbMath0273.10043OpenAlexW2010820459MaRDI QIDQ2264804

Harald Niederreiter, Walter Philipp

Publication date: 1973

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-73-04055-6

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Large deviations (60F10) Distribution modulo one (11J71) General theory of distribution modulo (1) (11K06)

Related Items (22)

General discrepancy estimates. III: The Erdös-Turán-Koksma inequality for the Haar function system ⋮ On the Erdős-Turán inequality on uniform distribution. I ⋮ On the Erdős-Turán inequality on uniform distribution. II ⋮ Berry-Esseen smoothing inequality for the Wasserstein metric on compact Lie groups ⋮ On the inequalities of Erdős-Turán and Berry-Esseen. I ⋮ On measures of uniformly distributed sequences and Benford's law ⋮ The structure of popular difference sets ⋮ Erdős and the integers ⋮ Equidistribution of random walks on compact groups. II: The Wasserstein metric ⋮ A limit theorem for random sums modulo 1 ⋮ Berry-Esseen bounds and Diophantine approximation ⋮ Pseudo-random numbers and optimal coefficients ⋮ Further discrepancy bounds and an Erdös-Turán-Koksma inequality for hybrid sequences ⋮ Van der Corput's difference theorem ⋮ On the Distribution of Pseudo-Random Numbers Generated by the Linear Congruential Method. II ⋮ On the orbits of multiplicative pairs ⋮ Quasi-Monte Carlo methods and pseudo-random numbers ⋮ On the distribution of roots of polynomials in sectors. II ⋮ A Uniform Distribution Question Related to Numerical Analysis ⋮ Convergence of random walks on the circle generated by an irrational rotation ⋮ On the Distribution of Pseudo-Random Numbers Generated by the Linear Congruential Method. III ⋮ Some extremal functions in Fourier analysis

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