A. Ferraguti

activity

20142026

most citedIrreducible compositions of degree two polynomials over finite fields have regular structure

14 citations · 45 across the 15 of their papers we have counts for

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18 papers · 1 filter

math.NT2026

$\Kab$ has the Bogomolov property for canonical heights

Andrea Ferraguti, Carlo Pagano

We show that for any number field $K$ and any rational map $f$ in $K (x)$ that is not conjugate to a power, (signed) Chebyshev or Lattès map, then $K^{ab}$ has the strong B…

math.NT2026

Abelian dynamical Galois groups over global function fields

Andrea Ferraguti, Patrick Ingram, Carlo Pagano

We establish a function field analogue of a recent conjecture of Andrews--Petsche. Our main result characterizes abelian dynamical Galois groups to be precisely the isotrivial ones…

math.NT2026

On the dynamical Galois group of certain affine polynomials in positive characteristic

Andrea Ferraguti, Guido Maria Lido

We use explicit class field theory of rational function fields to prove a dynamical criterion for a polynomial of the form $x^{p^{r}} + a x + b$ over a field of characteristic $p$ to have…

math.NT2023

Abelian dynamical Galois groups for unicritical polynomials

Andrea Ferraguti, Carlo Pagano

Andrews and Petsche proposed in 2020 a conjectural characterization of all pairs $(f, α)$ , where $f$ is a polynomial over a number field $K$ and $α \in K$ , such that the dynamical Ga…

math.NT2022★ 1 cited

A survey on abelian dynamical Galois groups

A. Ferraguti

Let $K$ be a number field, $f \in K [x]$ and $α \in K$ . A recent conjecture of Andrews and Petsche predicts that the dynamical Galois group of the pair $(f, α)$ is abelian if and only…

math.NT2022

Cyclotomic and abelian points in backward orbits of rational functions

Andrea Ferraguti, Alina Ostafe, Umberto Zannier

We prove several results on backward orbits of rational functions over number fields. First, we show that if $K$ is a number field, $ϕ \in K (x)$ and $α \in K$ then the extension of $…

math.NT2020

Constraining images of quadratic arboreal representations

Andrea Ferraguti, Carlo Pagano

In this paper, we prove several results on finitely generated dynamical Galois groups attached to quadratic polynomials. First we show that, over global fields, quadratic post-crit…

math.NT2020

Exceptional scatteredness in prime degree

Andrea Ferraguti, Giacomo Micheli

Let $q$ be an odd prime power and $n$ be a positive integer. Let $ℓ \in F_{q^{n}} [x]$ be a $q$ -linearised $t$ -scattered polynomial of linearized degree $r$ . Let $d=\max\{t,…

math.NT2019★ 4 cited

The inverse problem for arboreal Galois representations of index two

Andrea Ferraguti, Carlo Pagano, Daniele Casazza

This paper introduces a systematic approach towards the inverse problem for arboreal Galois representations of finite index attached to quadratic polynomials. Let $F$ be a field of…

math.NT2019

An equivariant isomorphism theorem for mod $p$ reductions of arboreal Galois representations

Andrea Ferraguti, Giacomo Micheli

Let $ϕ$ be a quadratic, monic polynomial with coefficients in $O_{F, D} [t]$ , where $O_{F, D}$ is a localization of a number ring $O_{F}$ . In this paper, we f…

math.NT2018

Full Classification of permutation rational functions and complete rational functions of degree three over finite fields

Andrea Ferraguti, Giacomo Micheli

Let $q$ be a prime power, $F_{q}$ be the finite field of order $q$ and $F_{q} (x)$ be the field of rational functions over $F_{q}$ . In this paper we classify all r…

math.NT2017

Strongly modular models of $Q$ -curves

Peter Bruin, Andrea Ferraguti

Let $E$ be a $Q$ -curve without complex multiplication. We address the problem of deciding whether $E$ is geometrically isomorphic to a strongly modular $Q$ -curve. W…

math.NT2017

The set of stable primes for polynomial sequences with large Galois group

Andrea Ferraguti

Let $K$ be a number field with ring of integers $O_{K}$ , and let ${f_{k}}_{k \in N} \subseteq O_{K} [x]$ be a sequence of monic polynomials such that for every $…

math.NT2017★ 14 cited

Irreducible compositions of degree two polynomials over finite fields have regular structure

Andrea Ferraguti, Giacomo Micheli, Reto Schnyder

Let $q$ be an odd prime power and $D$ be the set of monic irreducible polynomials in $F_{q} [x]$ which can be written as a composition of monic degree two polynomials. In this…

math.NT2016★ 10 cited

On sets of irreducible polynomials closed by composition

Andrea Ferraguti, Giacomo Micheli, Reto Schnyder

Let $S$ be a set of monic degree $2$ polynomials over a finite field and let $C$ be the compositional semigroup generated by $S$ . In this paper we establish a nec…

math.NT2016★ 4 cited

On the existence of infinite, non-trivial $F$ -sets

Andrea Ferraguti, Giacomo Micheli

In this paper we prove a conjecture of J. Andrade, S. J. Miller, K. Pratt and M. Trinh, showing the existence of a non trivial infinite $F$ -set over $F_{q} [x]$ for every fixe…

math.NT2015

On $L$ -functions of quadratic $Q$ -curves

Peter Bruin, Andrea Ferraguti

Let $K$ be a quadratic number field of discriminant $Δ_{K}$ , let $E$ be a $Q$ -curve without CM completely defined over $K$ and let $ω_{E}$ be an invariant differential on $E$ .…

math.NT2014★ 12 cited

On Mertens-Cesàro Theorem for Number Fields

Andrea Ferraguti, Giacomo Micheli

Let $K$ be a number field with ring of integers $O$ . After introducing a suitable notion of density for subsets of $O$ , generalizing that of natural density for s…

$\Kab$ has the Bogomolov property for canonical heights

Abelian dynamical Galois groups over global function fields

On the dynamical Galois group of certain affine polynomials in positive characteristic

Abelian dynamical Galois groups for unicritical polynomials

A survey on abelian dynamical Galois groups

Cyclotomic and abelian points in backward orbits of rational functions

Constraining images of quadratic arboreal representations

Exceptional scatteredness in prime degree

The inverse problem for arboreal Galois representations of index two

An equivariant isomorphism theorem for mod p reductions of arboreal Galois representations

Full Classification of permutation rational functions and complete rational functions of degree three over finite fields

Strongly modular models of Q-curves

The set of stable primes for polynomial sequences with large Galois group

Irreducible compositions of degree two polynomials over finite fields have regular structure

On sets of irreducible polynomials closed by composition

On the existence of infinite, non-trivial F-sets

On L-functions of quadratic Q-curves

On Mertens-Cesàro Theorem for Number Fields

An equivariant isomorphism theorem for mod $p$ reductions of arboreal Galois representations

Strongly modular models of $Q$ -curves

On the existence of infinite, non-trivial $F$ -sets

On $L$ -functions of quadratic $Q$ -curves