Additive Energy and Irregularities of Distribution-Reference-Cited by-同舟云学术

Additive Energy and Irregularities of Distribution

Published:2017-06-27 Issue:1 Volume:12 Page:99-107
ISSN:2309-5377
Container-title:Uniform distribution theory
language:en
Short-container-title:

Author:

Aistleitner Christoph¹,Larcher Gerhard²

Affiliation:

1. Institute of Financial Mathematics, and Applied Number Theory, University Linz, Altenbergerstraße 69, A-4040– Linz , Austria

2. Institute of Financial Mathematics, and Applied Number Theory, University Linz, Altenbergerstraße 69, A-4040- Linz , Austria

Abstract

Abstract We consider strictly increasing sequences (an)n≥1 of integers and sequences of fractional parts ({anα})n≥1 where α ∈ R. We show that a small additive energy of (an)n≥1 implies that for almost all α the sequence ({anα})n≥1 has large discrepancy. We prove a general result, provide various examples, and show that the converse assertion is not necessarily true.

Publisher

Walter de Gruyter GmbH

Reference15 articles.

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