35 citations · 163 across the 46 of their papers we have counts for
46 papers · 1 filter
Pencils of norm form equations and a conjecture of Thomas, II
Francesco Amoroso, David Masser, Umberto Zannier
We continue our studies on parametric norm forms , with lying in some parametric linear subvariety and integers sufficien…
Examples of effectivity for integral points on certain curves of genus 2
Pietro Corvaja, Davide Lombardo, Umberto Zannier
We consider families of smooth projective curves of genus 2 with a single point removed and study their integral points. We show that in many such families there is a dense set of…
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…
Rational distances from given rational points in the plane
Pietro Corvaja, Amos Turchet, Umberto Zannier
In this paper we study sets of points in the plane with rational distances from r prescribed points P_1, ...,P_r. A crucial case arises for r = 3, where we provide simple necessary…
Purely exponential parametrizations and their group-theoretic applications
Pietro Corvaja, Julian Demeio, Andrei Rapinchuk +2
This paper is mainly motivated by the analysis of the so-called Bounded Generation property (BG) of linear groups (in characteristic ), which is known to admit far-reaching grou…
Examples of effectivity for integral points on certain curves of genus 2
Pietro Corvaja, Umberto Zannier
This short article concerns a method to obtain effectivity for the search of integral points on certain (sets of) curves of genus 2. More precisely, we wish to illustrate just an e…
D-finiteness, rationality, and height III: multivariate Pólya-Carlson dichotomy
Jason P. Bell, Shaoshi Chen, Khoa D. Nguyen +1
We prove a result that can be seen as an analogue of the Pólya-Carlson theorem for multivariate D-finite power series with coefficients in . In the special case t…
Finite Orbits in Surfaces with a Double Elliptic Fibration and Torsion Values of Sections
Pietro Corvaja, Jacob Tsimerman, Umberto Zannier
We consider surfaces with a double elliptic fibration, with two sections. We study the orbits under the induced translation automorphisms proving that, under natural conditions, th…
D-finiteness, rationality, and height II: lower bounds over a set of positive density
Jason P. Bell, Khoa D. Nguyen, Umberto Zannier
We consider D-finite power series with coefficients in a number field . We show that there is a dichotomy governing the behaviour of as a function o…
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 is a number field, and then the extension of $…
Bounded Generation by semi-simple elements: quantitative results
Pietro Corvaja, Julian Demeio, Andrei Rapinchuk +2
We prove that for a number field , the distribution of the points of a set with a purely exponential parametrization, for example a set of matrices bou…
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 , with $A,B,D\in \ma…
Around the Chevalley-Weil Theorem
Pietro Corvaja, Amos Turchet, Umberto Zannier
We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological t…
Integral distances from (two) lattice points
Umberto Zannier
{\it .}We completely characterize pairs of lattice points in the plane with the property that there are infinitely many lattice points whose distance from both $P…
Finiteness theorems on elliptical billiards and a variant of the Dynamical Mordell-Lang Conjecture
Pietro Corvaja, Umberto Zannier
We offer some theorems, mainly of finiteness, for certain patterns in elliptical billiards, related to periodic trajectories. For instance, if two players hit a ball at a given pos…
On the distribution of rational points on ramified covers of abelian varieties
Pietro Corvaja, Julian Lawrence Demeio, Ariyan Javanpeykar +2
We prove new results on the distribution of rational points on ramified covers of abelian varieties over finitely generated fields of characteristic zero. For example, given a…
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…
On the -adic distribution of torsion values for a section of an abelian scheme
Brian Lawrence, Umberto Zannier
Let be an abelian scheme over a -adic field, and let be a section. We study the torsion locus $\bigcup \limits_{n \geq 1} s^{-1}(A[n…
D-finiteness, rationality, and height
Jason P. Bell, Khoa D. Nguyen, Umberto Zannier
Motivated by a result of van der Poorten and Shparlinski for univariate power series, Bell and Chen prove that if a multivariate power series over a field of characteristic 0 is D-…
A variant of the Mordell-Lang conjecture
Dragos Ghioca, Fei Hu, Thomas Scanlon +1
The Mordell-Lang conjecture (proven by Faltings, Vojta and McQuillan) states that the intersection of a subvariety of a semiabelian variety defined over an algebraically cl…
The Dynamical Mordell-Lang Conjecture for endomorphisms of semiabelian varieties defined over fields of positive characteristic
Pietro Corvaja, Dragos Ghioca, Thomas Scanlon +1
Let K be an algebraically closed field of prime characteristic p, let X be a semiabelian variety defined over a finite subfield of K, let f be a regular self-map on X defined over…
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…
On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem
Alina Ostafe, Min Sha, Igor E. Shparlinski +1
In this paper, we study multiplicative dependence of values of polynomials or rational functions over a number field. As an application, we obtain new results on multiplicative dep…
On abelian multiplicatively dependent points on a curve in a torus
Alina Ostafe, Min Sha, Igor E. Shparlinski +1
We show, under some natural conditions, that the set of abelian (and thus also cyclotomic) multiplicatively dependent points on an irreducible curve over a number field is a finite…