Ilaria Viglino

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math.NT2024

Arithmetic statistics of families of integer Sn-polynomials and application to class group torsion

Ilaria Viglino

We study the distributions of the splitting primes in certain families of number fields. The first and main example is the family Pn,N of integer polynomials monic of degree n with…

math.NT2024

An average version of Cilleruelo's conjecture for families of $S_{n}$ -polynomials over a number field

Ilaria Viglino

For $f \in Z [X]$ 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+\…

Arithmetic statistics of families of integer Sn-polynomials and application to class group torsion

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

An average version of Cilleruelo's conjecture for families of $S_{n}$ -polynomials over a number field