An average version of Cilleruelo's conjecture for families of $S_n$-polynomials over a number field

Ilaria Viglino

For $f\in \mathbb{Z}[X]$ an irreducible polynomial of degree $n$, the Cilleruelo's conjecture states that$$\log(\mbox{lcm}(f(1),\dots,f(M)))\sim(n-1)M\log M$$as $ M\rightarrow+\…