<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

Pubblicato online: 22 lug 2017

Pagine: 99 - 107

Ricevuto: 07 mar 2016

Accettato: 17 mar 2016

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

Parole chiave
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

Pubblicato online: 22 lug 2017

Pagine: 99 - 107

Ricevuto: 07 mar 2016

Accettato: 17 mar 2016

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

Parole chiavediscrepancy, additive energy, metric number theory, additive combinatorics

© 2017

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

Parole chiave
discrepancy, additive energy, metric number theory, additive combinatorics