Distribution modulo 1 of some oscillating sequences. III

D. Berend; Michael D. Boshernitzan; Grigori Kolesnik

doi:10.1023/A:1015678014546

Distribution modulo 1 of some oscillating sequences. III

D. Berend, Michael D. Boshernitzan, Grigori Kolesnik

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

For some oscillating functions, such as h(x) = x^π log³ x cos x, we consider the distribution properties modulo 1 (density, uniform distribution) of the sequence h(n), n ≧ 1. We obtain positive and negative results covering the case when the factor x^π log³ x is replaced by an arbitrary function f of at most polynomial growth belonging to any Hardy field. (The latter condition may be viewed as a regularity growth condition on f.) Similar results are obtained for the subsequence h(p), taken over the primes p = 2, 3, 5,....

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Acta Mathematica Hungarica
Volume	95
Issue number	1-2
DOIs	https://doi.org/10.1023/A:1015678014546
State	Published - 1 Apr 2002

Keywords

Density modulo 1
Distribution modulo 1
Exponential sums
Hardy field
Uniform distribution

ASJC Scopus subject areas

General Mathematics

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10.1023/A:1015678014546

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title = "Distribution modulo 1 of some oscillating sequences. III",

abstract = "For some oscillating functions, such as h(x) = xπ log3 x cos x, we consider the distribution properties modulo 1 (density, uniform distribution) of the sequence h(n), n ≧ 1. We obtain positive and negative results covering the case when the factor xπ log3 x is replaced by an arbitrary function f of at most polynomial growth belonging to any Hardy field. (The latter condition may be viewed as a regularity growth condition on f.) Similar results are obtained for the subsequence h(p), taken over the primes p = 2, 3, 5,....",

keywords = "Density modulo 1, Distribution modulo 1, Exponential sums, Hardy field, Uniform distribution",

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AU - Berend, D.

AU - Boshernitzan, Michael D.

AU - Kolesnik, Grigori

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N2 - For some oscillating functions, such as h(x) = xπ log3 x cos x, we consider the distribution properties modulo 1 (density, uniform distribution) of the sequence h(n), n ≧ 1. We obtain positive and negative results covering the case when the factor xπ log3 x is replaced by an arbitrary function f of at most polynomial growth belonging to any Hardy field. (The latter condition may be viewed as a regularity growth condition on f.) Similar results are obtained for the subsequence h(p), taken over the primes p = 2, 3, 5,....

AB - For some oscillating functions, such as h(x) = xπ log3 x cos x, we consider the distribution properties modulo 1 (density, uniform distribution) of the sequence h(n), n ≧ 1. We obtain positive and negative results covering the case when the factor xπ log3 x is replaced by an arbitrary function f of at most polynomial growth belonging to any Hardy field. (The latter condition may be viewed as a regularity growth condition on f.) Similar results are obtained for the subsequence h(p), taken over the primes p = 2, 3, 5,....

KW - Density modulo 1

KW - Distribution modulo 1

KW - Exponential sums

KW - Hardy field

KW - Uniform distribution

UR - https://www.scopus.com/pages/publications/0035982750

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DO - 10.1023/A:1015678014546

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JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

IS - 1-2

ER -

Distribution modulo 1 of some oscillating sequences. III

Abstract

Keywords

ASJC Scopus subject areas

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