Asymptotic behavior of the least common multiple of consecutive reducible quadratic progression terms

Abstract: Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $f(x)$ be the product of two linear polynomials with integer coefficients. In this paper, we show that $\log {\rm lcm}_{mn<i\le ln}{f(i)}=An+o(n)$, where $A$ is a constant depending only on $l$, $m$ and $f$.