L. Capuano

activity

20142026

most citedAn effective criterion for periodicity of l-adic continued fractions

22 citations · 62 across the 12 of their papers we have counts for

collaborators

18 papers

math.NT2026

Degeneracy loci and unlikely intersections in abelian schemes

Fabrizio Barroero, Laura Capuano, Tangli Ge +1

Let $A \to S$ be an abelian scheme over a normal quasi-projective variety over a number field, and let $X \subseteq A$ be a positive-dimensional subvarie…

math.NT2026

Singular intersections in split semiabelian varieties

Francesco Ballini, Laura Capuano, Nicola Ottolini

Let $G$ be a split semiabelian variety of dimension $n \geq 2$ and let $C \subset G$ an irreducible curve, where everything is defined over $\overline{\ma…

math.NT2025

If a machine did it, it is probably transcendental (even $p$ -adically)

Laura Capuano, Sara Checcoli, Marzio Mula +1

Continued fraction expansions provide a well-established bridge between algebraic properties of numbers and combinatorics on words. In this article, we investigate the algebraicity…

math.NT2024

p-Adically convergent loci in varieties arising from periodic continued fractions

Laura Capuano, Marzio Mula, Lea Terracini +1

Inspired by several alternative definitions of continued fraction expansions for elements in $Q_{p}$ , we study $p$ -adically convergent periodic continued fractions with parti…

math.NT2023

On $P$ -adic continued fractions with extraneous denominators: some explicit finiteness results

Laura Capuano, Sara Checcoli, Marzio Mula +1

Let $K$ be a number field. We show that, up to allowing a finite set of denominators in the partial quotients, it is possible to define algorithms for $P$ -adic continued…

math.NT2022

Quaternionic $p$ -adic continued fractions

Laura Capuano, Marzio Mula, Lea Terracini

We develop a theory of $p$ -adic continued fractions for a quaternion algebra $B$ over $Q$ ramified at a rational prime $p$ . Many properties holding in the commutative case…

math.NT2022★ 1 cited

Greatest Common Divisor results on semiabelian varieties and a Conjecture of Silverman

Fabrizio Barroero, Laura Capuano, Amos Turchet

A divisibility sequence is a sequence of integers ${d_{n}}$ such that $d_{m}$ divides $d_{n}$ if $m$ divides $n$ . Results of Bugeaud, Corvaja, Zannier, among others, have shown that th…

math.NT2021

Betti maps, Pell equation in polynomials and almost Belyi maps

Fabrizio Barroero, Laura Capuano, Umberto Zannier

We study the Betti map of a particular (but relevant) section of the family of Jacobians of hyperelliptic curves using the polynomial Pell equation $A^{2} - D B^{2} = 1$ , with $A,B,D\in \ma…

math.NT2021★ 2 cited

On the finiteness of $P$ -adic continued fractions for number fields

Laura Capuano, Nadir Murru, Lea Terracini

For a prime ideal $P$ of the ring of integers of a number field $K$ , we give a general definition of $P$ -adic continued fraction, which also includes classica…

math.NT2020★ 1 cited

On periodicity of $p$ -adic Browkin continued fractions

Laura Capuano, Nadir Murru, Lea Terracini

The classical theory of continued fractions has been widely studied for centuries for its important properties of good approximation, and more recently it has been generalized to $…

math.NT2020

Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes

Fabrizio Barroero, Laura Capuano, László Mérai +2

For positive integers $K$ and $L$ , we introduce and study the notion of $K$ -multiplicative dependence over the algebraic closure $F_{p}$ of a finite prime field $…

math.NT2020

A note on cyclotomic polynomials and Linear Feedback Shift Registers

Laura Capuano, Antonio J. Di Scala

Linear Feedback Shift Registers (LFRS) are tools commonly used in cryptography in many different context, for example as pseudo-random numbers generators. In this paper we characte…

math.NT2018★ 22 cited

An effective criterion for periodicity of l-adic continued fractions

Laura Capuano, Francesco Veneziano, Umberto Zannier

The theory of continued fractions has been generalized to l-adic numbers by several authors and presents many differences with respect to the real case. In the present paper we inv…

math.NT2018★ 8 cited

Unlikely Intersections in families of abelian varieties and the polynomial Pell equation

Fabrizio Barroero, Laura Capuano

Let S be a smooth irreducible curve defined over a number field k and consider an abelian scheme A over S and a curve C inside A, both defined over k. In previous works, we proved…

math.NT2016

Unlikely intersections in products of families of elliptic curves and the multiplicative group

Fabrizio Barroero, Laura Capuano

Let $E_{λ}$ be the Legendre elliptic curve of equation $Y^{2} = X (X - 1) (X - λ)$ . We recently proved that, given $n$ linearly independent points $P_{1} (λ), \dots, P_{n} (λ)$ on $E_{λ}$ with coordina…

math.NT2015★ 11 cited

Rational points on Grassmannians and unlikely intersections in tori

Laura Capuano, David Masser, Jonathan Pila +1

In this paper, we present an alternative proof of a finiteness theorem due to Bombieri, Masser and Zannier concerning intersections of a curve in the multiplicative group of dimens…

math.NT2014★ 15 cited

Linear relations in families of powers of elliptic curves

Fabrizio Barroero, Laura Capuano

Motivated by recent work of Masser and Zannier on simultaneous torsion on the Legendre elliptic curve $E_{λ}$ of equation $Y^{2} = X (X - 1) (X - λ)$ , we prove that, given $n$ linearly indepen…

math.NT2014★ 2 cited

Upper ramification jumps in abelian extensions of exponent p

Laura Capuano, Ilaria Del Corso

In this paper we present a classification of the possible upper ramification jumps for an elementary abelian p-extension of a p-adic field. The fundamental step for the proof of th…

Degeneracy loci and unlikely intersections in abelian schemes

Singular intersections in split semiabelian varieties

If a machine did it, it is probably transcendental (even p-adically)

p-Adically convergent loci in varieties arising from periodic continued fractions

On P-adic continued fractions with extraneous denominators: some explicit finiteness results

Quaternionic p-adic continued fractions

Greatest Common Divisor results on semiabelian varieties and a Conjecture of Silverman

Betti maps, Pell equation in polynomials and almost Belyi maps

On the finiteness of P-adic continued fractions for number fields

On periodicity of p-adic Browkin continued fractions

Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes

A note on cyclotomic polynomials and Linear Feedback Shift Registers

An effective criterion for periodicity of l-adic continued fractions

Unlikely Intersections in families of abelian varieties and the polynomial Pell equation

Unlikely intersections in products of families of elliptic curves and the multiplicative group

Rational points on Grassmannians and unlikely intersections in tori

Linear relations in families of powers of elliptic curves

Upper ramification jumps in abelian extensions of exponent p

If a machine did it, it is probably transcendental (even $p$ -adically)

On $P$ -adic continued fractions with extraneous denominators: some explicit finiteness results

Quaternionic $p$ -adic continued fractions

On the finiteness of $P$ -adic continued fractions for number fields

On periodicity of $p$ -adic Browkin continued fractions