Ilaria Viglino

activity

20222026

collaborators

4 papers

math.NT2026

Least common multiples of polynomial values: averaging, ray classes, and Galois statistics

Ilaria Viglino

We study analogues over number fields and the probabilistic congruence input that enters averaged versions of this problem. We prove an asymptotic formula for the least common mult…

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+\…

math.NT2022

Towards a generalization of the van der Waerden's conjecture for Sn-polynomials with integral coefficients over a fixed number field extension

Ilaria Viglino

The van der Waerden's Conjecture states that the set $P_{n, N}^{0} (Q)$ of monic integer polynomials $f (X)$ of degree $n$ , with height $\leq N$ such that the Galois g…

math.NT2022

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…

Least common multiples of polynomial values: averaging, ray classes, and Galois statistics

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

Towards a generalization of the van der Waerden's conjecture for Sn-polynomials with integral coefficients over a fixed number field extension

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

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