Complete uniform distribution of some oscillating sequences

D. Berend; G. Kolesnik

Complete uniform distribution of some oscillating sequences

D. Berend
, G. Kolesnik

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

1 Scopus citations

Abstract

Our main result is that the sequence (P(n) cos nα), n = 1, 2, ⋯, is completely uniformly distributed modulo 1 for any non-constant polynomial P and α with cos α transcendental. It follows as a very special case of our results that, if λ is a Salem number of degree 4, then the sequence (nλⁿ)_n=0^∞ is uniformly distributed modulo 1.

Original language	English
Pages (from-to)	127-144
Number of pages	18
Journal	Journal of the Ramanujan Mathematical Society
Volume	26
Issue number	2
State	Published - 1 Jun 2011

ASJC Scopus subject areas

General Mathematics

Cite this

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title = "Complete uniform distribution of some oscillating sequences",

abstract = "Our main result is that the sequence (P(n) cos nα), n = 1, 2, ⋯, is completely uniformly distributed modulo 1 for any non-constant polynomial P and α with cos α transcendental. It follows as a very special case of our results that, if λ is a Salem number of degree 4, then the sequence (nλn)n=0∞ is uniformly distributed modulo 1.",

author = "D. Berend and G. Kolesnik",

year = "2011",

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day = "1",

language = "English",

volume = "26",

pages = "127--144",

journal = "Journal of the Ramanujan Mathematical Society",

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T1 - Complete uniform distribution of some oscillating sequences

AU - Berend, D.

AU - Kolesnik, G.

PY - 2011/6/1

Y1 - 2011/6/1

N2 - Our main result is that the sequence (P(n) cos nα), n = 1, 2, ⋯, is completely uniformly distributed modulo 1 for any non-constant polynomial P and α with cos α transcendental. It follows as a very special case of our results that, if λ is a Salem number of degree 4, then the sequence (nλn)n=0∞ is uniformly distributed modulo 1.

AB - Our main result is that the sequence (P(n) cos nα), n = 1, 2, ⋯, is completely uniformly distributed modulo 1 for any non-constant polynomial P and α with cos α transcendental. It follows as a very special case of our results that, if λ is a Salem number of degree 4, then the sequence (nλn)n=0∞ is uniformly distributed modulo 1.

UR - https://www.scopus.com/pages/publications/85032187220

M3 - Article

AN - SCOPUS:85032187220

SN - 0970-1249

VL - 26

SP - 127

EP - 144

JO - Journal of the Ramanujan Mathematical Society

JF - Journal of the Ramanujan Mathematical Society

IS - 2

ER -

Complete uniform distribution of some oscillating sequences

Abstract

ASJC Scopus subject areas

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