The least common multiple of a sequence of products of linear polynomials

TL;DR

This paper investigates the asymptotic behavior of the least common multiple of a sequence generated by products of linear polynomials with integer coefficients, establishing a linear growth rate in the logarithm of the LCM.

Contribution

It provides an asymptotic estimate for the logarithm of the LCM of values of a polynomial product sequence, extending understanding of LCM growth for such sequences.

Findings

curate asymptotic estimate for log lcm(f(1), ..., f(n))

constant A depends on the polynomial f

logarithmic growth rate of the LCM as n limits

Abstract

Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty $, where $A$ is a constant depending on $f$.