On the Density of Coprime Tuples of the Form (n, ⌊f_1(n)⌋, …, ⌊f_k(n)⌋), Where f_1, …, f_k Are Functions from a Hardy Field
2017
Abstract
Let k∈N and let f_1, …, f_k belong to a Hardy field. We prove that under some natural conditions on the k-tuple ( f_1, …, f_k ) the density of the set {n∈N:gcd(n,⌊f_1(n)⌋,…,⌊f_k(n)⌋)=1} exists and equals 1/ζ(k+1), where ζ is the Riemann zeta function.
Details
Title
On the Density of Coprime Tuples of the Form (n, ⌊f_1(n)⌋, …, ⌊f_k(n)⌋), Where f_1, …, f_k Are Functions from a Hardy Field
Author(s)
Bergelson, Vitaly ; Richter, Florian Karl
Published in
Number Theory – Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy’s 60th Birthday
Pages
109-135
Date
2017
Publisher
Cham, Springer International Publishing
ISBN
978-3-319-55357-3
Other identifier(s)
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Laboratories
ERG
Record Appears in
Scientific production and competences > SB - School of Basic Sciences > MATH - Institute of Mathematics > ERG - Chair of Ergodic Theory
Work outside EPFL
Book chapters
Published
Work outside EPFL
Book chapters
Published
Record creation date
2021-11-26