Density modulo 1 and Hardy fields

Michel Abramoff, Daniel Berend, Grigori Kolesnik

Research output: Contribution to journalArticlepeer-review

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 (f(n))n=1 is dense modulo 1 in Rd, the sequence (2m3nα, f(n))m,n≥1 is dense modulo 1 in Rd+1 for irrational α. Some negative results concerning Furstenberg’s theorem are obtained as well.

Original languageEnglish
JournalIsrael Journal of Mathematics
DOIs
StateAccepted/In press - 1 Jan 2024

ASJC Scopus subject areas

  • General Mathematics

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