<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

Publié en ligne: 22 juil. 2017

Pages: 99 - 107

Reçu: 07 mars 2016

Accepté: 17 mars 2016

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

Mots clés
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

Publié en ligne: 22 juil. 2017

Pages: 99 - 107

Reçu: 07 mars 2016

Accepté: 17 mars 2016

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

Mots clésdiscrepancy, additive energy, metric number theory, additive combinatorics

© 2017

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

Mots clés
discrepancy, additive energy, metric number theory, additive combinatorics