Home / Journals / Uniform Distribution Theory (UDT) / UDT. Volume 19. Issue 1 & 2 / On the Connection Between the Beurling-Malliavin Density and the Asymptotic Density

Uniform Distribution Theory
CC: Creative Commons BY: credit must be given to the creator. ND: No derivatives or adaptations of the work are permitted.

Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 19. Issue 1 & 2


Published on

December, 2024


Pages

67-86


DOI

https://doi.org/10.2478/udt-2024-0006

Article

On the Connection Between the Beurling-Malliavin Density and the Asymptotic Density


Authors

Rita Giuliano and Georges Grekos


Abstract

We study the notion of Beurling-Malliavin density from the point of view of Number Theory. We prove a general relation between the Beurling-Malliavin density and the upper asymptotic density; we identify a class of sequences for which the two densities coincide; this class contains the arithmetic progressions. Last, by means of an alternative definition of Beurling-Malliavin density, we study the connection with the asymptotic density for another kind of sequences that again generalizes the arithmentic progressions.


Citation

Giuliano, R. & Grekos, G. (2024). On the Connection Between the Beurling-Malliavin Density and the Asymptotic Density. Uniform distribution theory, 19(1-2), 67-86. https://doi.org/10.2478/udt-2024-0006