The Beurling-Malliavin density, the Pólya density and their connection

In this paper we present a new formulation of the Beurling-Malliavin density (Proposition 1). Then we consider the upper Pólya density and show how its existence is connected with the concept of subadditivity; moreover, by means of some quantities introduced for proving Proposition 1, a theorem is p...

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Bibliographic Details
Published in:Uniform distribution theory 2024, Vol.19 (1), p.43-66
Main Authors: Giuliano, Rita, Grekos, Georges, Misik, Ladislav
Format: Article
Language:English
Subjects:
Mathematics
Number Theory
Online Access:Get full text
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Summary:In this paper we present a new formulation of the Beurling-Malliavin density (Proposition 1). Then we consider the upper Pólya density and show how its existence is connected with the concept of subadditivity; moreover, by means of some quantities introduced for proving Proposition 1, a theorem is presented that clarifies the connection between the upper Pólya and the Beurling-Malliavin densities. In the last section we discuss the classical definition of the upper Pólya density and we prove a result which seems to be new.
ISSN:2309-5377
1336-913X