On the greatest common divisor of integer parts of polynomials
Number Theory
2023-12-05 v3
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 and integer parts of polynomials evaluated at . The error terms in our formulas are of various strengths depending on the Diophantine properties of the leading coefficients of these polynomials.
Keywords
Cite
@article{arxiv.2205.00253,
title = {On the greatest common divisor of integer parts of polynomials},
author = {William Banks and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:2205.00253},
year = {2023}
}