On the error term of the logarithm of the lcm of a quadratic sequence

TL;DR

This paper investigates the error term in the asymptotic formula for the logarithm of the least common multiple of the quadratic sequence n^2+1, utilizing distribution results of roots modulo primes.

Contribution

It provides a detailed analysis of the error term in the asymptotic behavior of the lcm of quadratic sequences, extending previous results by Cilleruelo.

Findings

Derived explicit bounds for the error term

Connected root distribution of quadratic polynomials to lcm asymptotics

Enhanced understanding of number theoretic properties of quadratic sequences

Abstract

We study the logarithm of the least common multiple of the sequence of integers given by $1^2+1, 2^2+1,..., n^2+1$. Using a result of Homma on the distribution of roots of quadratic polynomials modulo primes we calculate the error term for the asymptotics obtained by Cilleruelo.