### 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 = min_{K}K^{-1} + ∑^{K - 1}_{k = 1} |α_{k}|/k, where the α_{k} are the Fourier coefficients. We investigate how bad this estimate can be. We prove that in the worst case Δ is of order B^{3/2}.

Original language | English |
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Pages (from-to) | 84-88 |

Number of pages | 5 |

Journal | Journal of Number Theory |

Volume | 49 |

Issue number | 1 |

DOIs | |

Publication status | Published - Oct 1994 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

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

Research output: Contribution to journal › Article

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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 -