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Categoría del artículo: Dedicated to the fifth international conference on Uniform Distribution Theory (UDT 2016) Sopron, Hungary, July 5–8, 2016
Publicado en línea: 22 jul 2017
Páginas: 99 - 107
Recibido: 07 mar 2016
Aceptado: 17 mar 2016
DOI: https://doi.org/10.1515/udt-2017-0006
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© 2017
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
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.