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

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

Bergelson V
Richter F

Springer International Publishing, (2017), 109-135

DOI: 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.

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Bergelson, V., & Richter, F. K. (2017). On the density of coprime tuples of the form (n, [f1(n)],...,[fk(n)]), where f1,...,fk 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

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

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