<abstract xmlns="http://www.w3.org/1999/xhtml"> 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. </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.

Additive Energy and Irregularities of Distribution

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Additive Energy and Irregularities of Distribution"}

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...

Additive Energy and Irregularities of Distribution

Article Category: Dedicated to the fifth international conference on Uniform Distribution Theory (UDT 2016) Sopron, Hungary, July 5–8, 2016

Online veröffentlicht: 22. Juli 2017

Seitenbereich: 99 - 107

Eingereicht: 07. März 2016

Akzeptiert: 17. März 2016

DOI: https://doi.org/10.1515/udt-2017-0006

Schlüsselwörter
discrepancy, additive energy, metric number theory, additive combinatorics

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Additive Energy and Irregularities of Distribution

Article Category: Dedicated to the fifth international conference on Uniform Distribution Theory (UDT 2016) Sopron, Hungary, July 5–8, 2016

Online veröffentlicht: 22. Juli 2017

Seitenbereich: 99 - 107

Eingereicht: 07. März 2016

Akzeptiert: 17. März 2016

DOI: https://doi.org/10.1515/udt-2017-0006

Schlüsselwörterdiscrepancy, additive energy, metric number theory, additive combinatorics

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Schlüsselwörter
discrepancy, additive energy, metric number theory, additive combinatorics