22 citations · 51 across the 16 of their papers we have counts for
17 papers
On the Disk of Convergence of Algebraic Power Series
Francesco Veneziano, Umberto Zannier
This paper is mainly concerned with the disk of convergence of a power series s(x) representing an algebraic function of x and specifically with the relation between this disk and…
The field of iterates of a rational function
Francesco Veneziano, Solomon Vishkautsan
We study how the field of definition of a rational function changes under iteration. We provide a complete classification of polynomials with the property that the field of definit…
Classification of rational angles in plane lattices II
Roberto Dvornicich, Davide Lombardo, Francesco Veneziano +1
This paper is a continuation of an earlier one, and completes a classification of the configurations of points in a plane lattice that determine angles that are rational multiples…
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 , we study -adically convergent periodic continued fractions with parti…
Hyperelliptic continued fractions in the singular case of genus zero
Francesco Ballini, Francesco Veneziano
It is possible to define a continued fraction expansion of elements in a function field of a curve by expanding as a Laurent series in a local parameter. Considering the square roo…
A note on the zeroes of the Fredholm series
Umberto Zannier, Francesco Veneziano
The issue had been raised whether the Fredholm series has infinitely many zeroes in the unit disk. We provide an affirmative answer, proving that in fact ev…
Explicit height bounds for -rational points on transverse curves in powers of elliptic curves
Francesco Veneziano, Evelina Viada
Let be an algebraic curve embedded transversally in a power of an elliptic curve . In this article we produce a good explicit bound for the height of all the algebraic…
Classification of rational angles in plane lattices
Roberto Dvornicich, Francesco Veneziano, Umberto Zannier
This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of . We shall study how many such angles may appear i…
Finiteness and periodicity of continued fractions over quadratic number fields
Zuzana Masáková, Tomáš Vávra, Francesco Veneziano
We consider continued fractions with partial quotients in the ring of integers of a quadratic number field and we prove a generalization to such continued fractions of the clas…
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…
A sharp Bogomolov-type bound
Sara Checcoli, Francesco Veneziano, Evelina Viada
We prove a sharp lower bound for the essential minimum of a non-translate variety in certain abelian varieties. This uses and generalises a result of Galateau. Our bound is a new s…
On the Explicit Torsion Anomalous Conjecture
Sara Checcoli, Francesco Veneziano, Evelina Viada
The Torsion Anomalous Conjecture states that an irreducible variety embedded in a semi-abelian variety contains only finitely many maximal -torsion anomalous varieties. In t…
The explicit Mordell Conjecture for families of curves (with an appendix by M. Stoll)
Sara Checcoli, Francesco Veneziano, Evelina Viada
In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on cu…
Pisot unit generators in number fields
Tomáš Vávra, Francesco Veneziano
Pisot numbers are real algebraic integers bigger than 1, whose other conjugates have all modulus smaller than 1. In this paper we deal with the algorithmic problem of finding the s…
On the integral values of a curious recurrence
Roberto Dvornicich, Francesco Veneziano, Umberto Zannier
We discuss a problem initially thought for the Mathematical Olympiad but which has several interpretations. The recurrence sequences involved in this problem may be generalized to…
On torsion anomalous intersections
Sara Checcoli, Francesco Veneziano, Evelina Viada
A deep conjecture on torsion anomalous varieties states that if is a weak-transverse variety in an abelian variety, then the complement of all -torsion anomalous va…
Quadratic integral solutions to double Pell equations
Francesco Veneziano
We study the quadratic integral points-that is, (S-)integral points defined over any extension of degree two of the base field-on a curve defined in P_3 by a system of two Pell equ…