TY - JOUR
T1 - Density modulo 1 and Hardy fields
AU - Abramoff, Michel
AU - Berend, Daniel
AU - Kolesnik, Grigori
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/1/1
Y1 - 2024/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85211462226&partnerID=8YFLogxK
U2 - 10.1007/s11856-024-2696-8
DO - 10.1007/s11856-024-2696-8
M3 - Article
AN - SCOPUS:85211462226
SN - 0021-2172
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
ER -