On an Inequality of Erdo{combining double acute accent}s and Turán Concerning Uniform Distribution Modulo One, II

Research output: Contribution to journalArticle

Abstract

A famous inequality of Erdo{combining double acute accent}s and Turán estimates the discrepancy Δ of a finite sequence of real numbers by the quantity B = minKK-1 + ∑K - 1k = 1k|/k, where the αk are the Fourier coefficients. We investigate how bad this estimate can be. We prove that in the worst case Δ is of order B3/2.

Original languageEnglish
Pages (from-to)84-88
Number of pages5
JournalJournal of Number Theory
Volume49
Issue number1
DOIs
Publication statusPublished - Oct 1994

Fingerprint

Uniform distribution
Acute
Modulo
Fourier coefficients
Estimate
Discrepancy

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

@article{f3e469701b4747e8bb6d6041ef1326df,
title = "On an Inequality of Erdo{combining double acute accent}s and Tur{\'a}n Concerning Uniform Distribution Modulo One, II",
abstract = "A famous inequality of Erdo{combining double acute accent}s and Tur{\'a}n estimates the discrepancy Δ of a finite sequence of real numbers by the quantity B = minKK-1 + ∑K - 1k = 1 |αk|/k, where the αk are the Fourier coefficients. We investigate how bad this estimate can be. We prove that in the worst case Δ is of order B3/2.",
author = "I. Ruzsa",
year = "1994",
month = "10",
doi = "10.1006/jnth.1994.1082",
language = "English",
volume = "49",
pages = "84--88",
journal = "Journal of Number Theory",
issn = "0022-314X",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - On an Inequality of Erdo{combining double acute accent}s and Turán Concerning Uniform Distribution Modulo One, II

AU - Ruzsa, I.

PY - 1994/10

Y1 - 1994/10

N2 - A famous inequality of Erdo{combining double acute accent}s and Turán estimates the discrepancy Δ of a finite sequence of real numbers by the quantity B = minKK-1 + ∑K - 1k = 1 |αk|/k, where the αk are the Fourier coefficients. We investigate how bad this estimate can be. We prove that in the worst case Δ is of order B3/2.

AB - A famous inequality of Erdo{combining double acute accent}s and Turán estimates the discrepancy Δ of a finite sequence of real numbers by the quantity B = minKK-1 + ∑K - 1k = 1 |αk|/k, where the αk are the Fourier coefficients. We investigate how bad this estimate can be. We prove that in the worst case Δ is of order B3/2.

UR - http://www.scopus.com/inward/record.url?scp=43949152502&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43949152502&partnerID=8YFLogxK

U2 - 10.1006/jnth.1994.1082

DO - 10.1006/jnth.1994.1082

M3 - Article

AN - SCOPUS:43949152502

VL - 49

SP - 84

EP - 88

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -