On the Greatest Common Divisor of Integer Parts of Polynomials

William D. Banks, Igor E. Shparlinski

Type: Article

Publication Date: 2024-01-01

Citations: 0

DOI: https://doi.org/10.1307/mmj/20226243

Abstract

Motivated by a question of V. Bergelson and F. K. Richter (2017), we obtain asymptotic formulas for the number of relatively prime tuples composed of positive integers n≤N and integer parts of polynomials evaluated at n. The error terms in our formulas are of various strengths depending on the Diophantine properties of the leading coefficients of these polynomials.

Locations

The Michigan Mathematical Journal - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (7)

Action	Title	Year	Authors
+	Zur metrischen Theorie der diophantischen Approximationen	1926	A. Khintchine
+	Rational approximations to algebraic numbers	1955	K. F. Roth
+ PDF Chat	On the probability that n and g(n) are relatively prime	1959	P. Erdős G. G. Lorentz
+ PDF Chat	On the Number of Primitive Lattice Points in a Parallelogram	1953	T. Estermann
+ PDF Chat	On Integers <i>n</i> Relatively Prime to [<i>αn</i>]	1953	G. L. Watson
+ PDF Chat	Weyl Sums over Integers with Digital Restrictions	2023	Igor E. Shparlinski Jörg Μ. Thuswaldner
+ PDF Chat	Corrigendum	1955	K. F. Roth