The least common multiple of a quadratic sequence

TL;DR

This paper derives an asymptotic estimate for the logarithm of the least common multiple of quadratic polynomial sequences, revealing its growth rate and a constant term depending on the polynomial.

Contribution

It provides a new asymptotic formula for the least common multiple of values of irreducible quadratic polynomials, extending understanding of their number-theoretic properties.

Findings

log l.c.m.(f(1),...,f(n)) = n log n + Bn + o(n)

B depends on the specific quadratic polynomial

The estimate improves previous bounds on quadratic sequences

Abstract

For any irreducible quadratic polynomial f(x) in Z[x] we obtain the estimate log l.c.m.(f(1),...,f(n))= n log n + Bn + o(n) where B is a constant depending on f.