Uniform distribution and Hardy fields

DOI10.1007/BF02835955zbMath0804.11046MaRDI QIDQ1326663

Michael D. Boshernitzan

Publication date: 18 May 1994

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

Hardy fieldreal functionuniform distribution mod 1approximation by rational polynomialsasymptotic distribution modulo 1dense mod 1

Mathematics Subject Classification ID

General theory of distribution modulo (1) (11K06)

Related Items (31)

Uniform distribution and Hardy fields ⋮ Van der Corput's difference theorem: some modern developments ⋮ Joint ergodicity of Hardy field sequences ⋮ Gaps in \(\sqrt{n}\bmod 1\) and ergodic theory ⋮ Diophantine properties of iets and general systems: quantitative proximality and connectivity ⋮ Some open problems on multiple ergodic averages ⋮ A random pointwise ergodic theorem with Hardy field weights ⋮ A Hardy field extension of Szemerédi's theorem ⋮ Distribution modulo 1 of some oscillating sequences. II ⋮ Equidistribution of sparse sequences on nilmanifolds ⋮ Plünnecke inequalities for countable abelian groups ⋮ On the Density of Coprime Tuples of the Form (n, ⌊ f 1(n)⌋, …, ⌊ f k (n)⌋), Where f 1, …, f k Are Functions from a Hardy Field ⋮ Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications ⋮ Additive bases arising from functions in a Hardy field ⋮ A generalization of van der Corput's difference theorem with applications to recurrence and multiple ergodic averages ⋮ Multiple recurrence and convergence for Hardy sequences of polynomial growth ⋮ Schrödinger operators with dynamically defined potentials ⋮ Uniform distribution in nilmanifolds along functions from a Hardy field ⋮ A polynomial-exponential variation of Furstenberg’s theorem ⋮ Joint ergodicity of sequences ⋮ Power bounded operators and the mean ergodic theorem for subsequences ⋮ (Uniform) convergence of twisted ergodic averages ⋮ A generalization of Kátai's orthogonality criterion with applications ⋮ Weighted multiple ergodic averages and correlation sequences ⋮ Distributions of finite sequences represented by polynomials in Piatetski-Shapiro sequences ⋮ Uniform distribution of subpolynomial functions along primes and applications ⋮ Numbers with complicated decimal expansions ⋮ Ergodic averaging sequences ⋮ A family of Schrödinger operators whose spectrum is an interval ⋮ Furstenberg systems of Hardy field sequences and applications ⋮ A multidimensional Szemerédi theorem for Hardy sequences of different growth

Cites Work

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• An extension of Hardy's class L of orders of infinity
• New orders of infinity
• Hardy fields
• Hardy fields and existence of transexponential functions
• Convex-invariant means and a pathwise central limit theorem
• The distribution of leading digits and uniform distribution mod 1
• Uniform distribution and Hardy fields
• Estimates for trigonometric sums by Vinogradov's method, and some applications
• A Note on Well Distributed Sequences
• Fractional iteration of exponentially growing functions
• The Rank of a Hardy Field
• "Orders of Infinity" Generated by Difference Equations
• Discrete "Orders of Infinity"
• Growth Properties of Functions in Hardy Fields
• Second Order Differential Equations over Hardy Fields
• Entire Functions and Uniform Distribution Modulo 1
• Strict Ergodicity and Transformation of the Torus
• Fonctions entières et répartition modulo un. II

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