On the density of coprime tuples of the form (n, [f1(n)],...,[fk(n)]), where f1,...,fk are functions from a hardy field

Vitaly Bergelson; Florian Karl Richter

doi:10.1007/978-3-319-55357-3_5

On the density of coprime tuples of the form (n, [f₁(n)],...,[f_k(n)]), where f₁,...,f_k are functions from a hardy field

Vitaly Bergelson^*, Florian Karl Richter

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

Abstract

Let k ε N and let f₁,...,f_k belong to a Hardy field. We prove that under some natural conditions on the k-tuple (f₁,...,f_k) the density of the set exists and equals where Z is the Riemann zeta function.

Original language	English (US)
Title of host publication	Number Theory - Diophantine Problems, Uniform Distribution and Applications
Subtitle of host publication	Festschrift in Honour of Robert F. Tichy's 60th Birthday
Publisher	Springer International Publishing
Pages	109-135
Number of pages	27
ISBN (Electronic)	9783319553573
ISBN (Print)	9783319553566
DOIs	https://doi.org/10.1007/978-3-319-55357-3_5
State	Published - Jun 1 2017

ASJC Scopus subject areas

Mathematics(all)

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10.1007/978-3-319-55357-3_5

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Bergelson, V., & Richter, F. K. (2017). On the density of coprime tuples of the form (n, [f₁(n)],...,[f_k(n)]), where f₁,...,f_k are functions from a hardy field. In Number Theory - Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday (pp. 109-135). Springer International Publishing. https://doi.org/10.1007/978-3-319-55357-3_5

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abstract = "Let k ε N and let f1,...,fk belong to a Hardy field. We prove that under some natural conditions on the k-tuple (f1,...,fk) the density of the set exists and equals where Z is the Riemann zeta function.",

author = "Vitaly Bergelson and Richter, {Florian Karl}",

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Bergelson, V & Richter, FK 2017, On the density of coprime tuples of the form (n, [f₁(n)],...,[f_k(n)]), where f₁,...,f_k are functions from a hardy field. in Number Theory - Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday. Springer International Publishing, pp. 109-135. https://doi.org/10.1007/978-3-319-55357-3_5

On the density of coprime tuples of the form (n, [f₁(n)],...,[f_k(n)]), where f₁,...,f_k are functions from a hardy field. / Bergelson, Vitaly; Richter, Florian Karl.
Number Theory - Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday. Springer International Publishing, 2017. p. 109-135.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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On the density of coprime tuples of the form (n, [f₁(n)],...,[f_k(n)]), where f₁,...,f_k are functions from a hardy field

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