Matteo Verzobio

activity

20182026

most citedPrimitive divisors of sequences associated to elliptic curves

5 citations · 18 across the 11 of their papers we have counts for

collaborators

12 papers

math.NT2026

Towards linear growth for biprojective hypersurfaces of small dimension

Tim Browning, Matteo Verzobio

After removing suitable thin subsets, we count rational points of bounded height on some hypersurfaces of small bidegree in $P^{3} \times P^{3}$ and in $\mathbb{P}^3\ti…

math.NT2025

Selmer groups of families of elliptic curves with an $ℓ$ -isogeny

Stephanie Chan, Matteo Verzobio

For certain families of elliptic curves admitting a rational isogeny of prime degree $ℓ$ , we establish a central limit theorem for the Tamagawa ratio and derive bounds on its av…

math.NT2025

The density of elliptic curves over $Q_{p}$ with a rational 3-torsion point or a rational 3-isogeny

Stevan Gajović, Lazar Radičević, Matteo Verzobio

We determine the probability that a random Weierstrass equation with coefficients in the $p$ -adic integers defines an elliptic curve with a non-trivial $3$ -torsion point, or with a…

math.NT2023

Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve

Stefan Barańczuk, Bartosz Naskręcki, Matteo Verzobio

Let $A$ be an abelian variety defined over a number field $K$ , $E / K$ be an elliptic curve, and $ϕ : A \to E^{m}$ be an isogeny defined over $K$ . Let $P \in A (K)$ be such that $ϕ(P)=(Q_1,…

math.NT2022★ 1 cited

On the local-global principle for isogenies of abelian surfaces

Davide Lombardo, Matteo Verzobio

Let $ℓ$ be a prime number. We classify the subgroups $G$ of $Sp_{4} (F_{ℓ})$ and $GSp_{4} (F_{ℓ})$ that act irreducibly on $\mathbb{F…

math.NT2022★ 2 cited

Common valuations of division polynomials

Bartosz Naskręcki, Matteo Verzobio

In this note we prove a formula for the cancellation exponent $k_{v, n}$ between division polynomials $ψ_{n}$ and $ϕ_{n}$ associated with a sequence ${n P}_{n \in N}$ of points…

math.NT2021★ 3 cited

A recurrence relation for elliptic divisibility sequences

Matteo Verzobio

In literature, there are two different definitions of elliptic divisibility sequences. The first one says that a sequence of integers ${h_{n}}_{n \geq 0}$ is an elliptic divisibilit…

math.NT2020★ 3 cited

Primitive divisors of sequences associated to elliptic curves with complex multiplication

Matteo Verzobio

Let $P$ and $Q$ be two points on an elliptic curve defined over a number field $K$ . For $α \in End (E)$ , define $B_{α}$ to be the $O_{K}$ -integral ideal generated by the…

math.NT2020★ 2 cited

Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728

Matteo Verzobio

Take a rational elliptic curve defined by the equation $y^{2} = x^{3} + a x$ in minimal form and consider the sequence $B_{n}$ of the denominators of the abscissas of the iterate of a non-tor…

math.NT2020★ 2 cited

Some effectivity results for primitive divisors of elliptic divisibility sequences

Matteo Verzobio

Let $P$ be a non-torsion point on an elliptic curve defined over a number field $K$ and consider the sequence ${B_{n}}_{n \in N}$ of the denominators of $x (n P)$ . We prove t…

math.NT2019★ 5 cited

Primitive divisors of sequences associated to elliptic curves

Matteo Verzobio

Let ${n P + Q}_{n \geq 0}$ be a sequence of points on an elliptic curve defined over a number field $K$ . In this paper, we study the denominators of the $x$ -coordinates of this sequen…

math.NT2018

On the $L$ -polynomials of curves over finite fields

Francesco Ballini, Davide Lombardo, Matteo Verzobio

We discuss, in a non-Archimedean setting, the distribution of the coefficients of $L$ -polynomials of curves of genus $g$ over $F_{q}$ . Among other results, this allows us to…

Towards linear growth for biprojective hypersurfaces of small dimension

Selmer groups of families of elliptic curves with an ℓ-isogeny

The density of elliptic curves over Qp​ with a rational 3-torsion point or a rational 3-isogeny

Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve

On the local-global principle for isogenies of abelian surfaces

Common valuations of division polynomials

A recurrence relation for elliptic divisibility sequences

Primitive divisors of sequences associated to elliptic curves with complex multiplication

Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728

Some effectivity results for primitive divisors of elliptic divisibility sequences

Primitive divisors of sequences associated to elliptic curves

On the L-polynomials of curves over finite fields

Selmer groups of families of elliptic curves with an $ℓ$ -isogeny

The density of elliptic curves over $Q_{p}$ with a rational 3-torsion point or a rational 3-isogeny

On the $L$ -polynomials of curves over finite fields