Work

Density modulo 1 and Hardy fields

Year: 2024

Type: article

Abstract: In this article we extend Boshernitzan’s result on density modulo 1 of sequences arising from functions belonging to a Hardy field. We also merge these results with Furstenberg’s ×2×3 theorem. We prove, for example, that, given a vector f of subpolynomial functions in a Hardy field, such that $$(\mathbf{f}(n))_{n=1}^{\infty}$$ ( f ( n ) ) n = 1 ∞ is dense modulo 1 in R d , the sequence (2 m 3 n α, f(n)) m,n≥1 is dense modulo 1 in R d+1 for irrational α. Some negative results concerning Furstenberg’s theorem are obtained as well.

Source: Israel Journal of Mathematics

DOI: 10.1007/s11856-024-2696-8

Authors: Michel Abramoff, Daniel Berend, Grigori Kolesnik

Institutions: Ben-Gurion University of the Negev, California State University Los Angeles

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Ben-Gurion University of the Negev