Well-distribution modulo one and the primes

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 23 Oct 2025Embargo end date: 01 Jan 2024 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society (issn: 0002-9939, eissn: 1088-6826,

Copyright policy )Funded by:NSERC | unidentified, NSF | FRG: Averages of L-functi..., NSF | Analytic Number Theory Mo... +1 projects

Authors: Champagne, J.; Lê, T. H.; Liu, Y. -R.; Wooley, T. D.;

doi: 10.1090/proc/17364 , 10.48550/arxiv.2406.19491

arXiv: 2406.19491

Well-distribution modulo one and the primes

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Abstract

Let ( p n ) (p_n) denote the sequence of prime numbers, ordered with 2 = p 1 > p 2 > … 2=p_1>p_2>\ldots . We demonstrate the existence of an irrational number α \alpha having the property that the sequence ( α p n ) (\alpha p_n) is not well-distributed modulo 1 1 .

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Keywords

Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT), 11K36, 11K06

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NSERC| unidentified, NSF| FRG: Averages of L-functions and Arithmetic Stratification, NSF| Analytic Number Theory Motivated by Approximate Translation Invariance, NSF| Additive and Combinatorial Problems in Groups