Randomness of the square root of 2 and the giant leap. I

DOI10.1007/s10998-010-2137-9zbMath1259.11092OpenAlexW2025653076MaRDI QIDQ1945262

József Beck

Publication date: 5 April 2013

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10998-010-2137-9

zbMATH Keywords

Dedekind sumscentral limit theoremcontinued fractionsdiscrepancydistribution modulo 1diophantine inequalitiesirregularities of distributioninhomogeneous linear formslattice point counting in specified regions

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Lattice points in specified regions (11P21) Irregularities of distribution, discrepancy (11K38) General theory of distribution modulo (1) (11K06)

Related Items (21)

Asymptotic windings of horocycles ⋮ On the convergence of Diophantine Dirichlet series ⋮ A temporal central limit theorem for real-valued cocycles over rotations ⋮ Local discrepancies in the problem of fractional parts distribution of a linear function ⋮ Some counterexamples to the central limit theorem for random rotations ⋮ Discrepancy skew products and affine random walks ⋮ On the metric upper density of Birkhoff sums for irrational rotations ⋮ Asymptotics and limit theorems for horocycle ergodic integrals à la Ratner (with an appendix by Emilio Corso) ⋮ Ergodic and Statistical Properties of $\B$-Free Numbers ⋮ Cauchy distributions for the integrable standard map ⋮ Fast and slow points of Birkhoff sums ⋮ The visits to zero of a random walk driven by an irrational rotation ⋮ The distribution of integers in a totally real cubic field ⋮ Temporal distributional limit theorems for dynamical systems ⋮ On the CLT for rotations and BV functions ⋮ Local discrepancies in the problem of the distribution of the sequence \(\{k\alpha\}\) ⋮ Birkhoff sum fluctuations in substitution dynamical systems ⋮ The Surprising Accuracy of Benford’s Law in Mathematics ⋮ No temporal distributional limit theorem for a.e. irrational translation ⋮ Pell equation and randomness ⋮ A note on the distributions of \((\log n) \bmod 1\)

Cites Work

• Discrepancy of the sequence \(\Big(\Big\{n{1+\sqrt{5}\over 2}\Big\}\Big)\)
• Another proof of a theorem of J. Beck
• Das Verhalten der Kleinschen Funktionen log(w1, w2) gegenüber Modultransformationen und verallgemeinerte Dedekindsche Summen.
• On successive settings of an arc on the circumference of a circle
• Notes on generalized Dedekind sums
• General analogues to the law of the iterated logarithm
• Irregularities of distribution, VII
• On irregularities of distribution
• Note on irregularities of distribution
• Randomness in lattice point problems
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