Zobrazeno 1 - 10
of 372
pro vyhledávání: '"Zannier, Umberto"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G11, Pp 1249-1255 (2022)
We prove that for a number field $F$, the distribution of the points of a set $\Sigma \subset \mathbb{A}_F^n$ with a purely exponential parametrization, for example a set of matrices boundedly generated by semi-simple (diagonalizable) elements, is of
Externí odkaz:
https://doaj.org/article/c5025fd882d440ce838592cc7c0a62f1
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 of ${\pi}$. We give a complete and explicit description of lattices ac
Externí odkaz:
http://arxiv.org/abs/2404.02559
In this paper we consider sets of points in the plane with rational distances from a prescribed finite set of $n$ rational points. We show that for $n\le 3$, the points are dense in the real topology. On the other hand, for $n\ge 4$, we show that the
Externí odkaz:
http://arxiv.org/abs/2403.02030
Autor:
Corvaja, Pietro, Zannier, Umberto
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 example of application of a criterion of Bilu, to derive effectivity fo
Externí odkaz:
http://arxiv.org/abs/2308.15505
This paper is mainly motivated by the analysis of the so-called Bounded Generation property (BG) of linear groups (in characteristic $0$), which is known to admit far-reaching group-theoretic implications. We achieve complete answers to certain longs
Externí odkaz:
http://arxiv.org/abs/2308.14013
We prove a result that can be seen as an analogue of the P\'olya-Carlson theorem for multivariate D-finite power series with coefficients in $\bar{\mathbb{Q}}$. In the special case that the coefficients are algebraic integers, our main result says th
Externí odkaz:
http://arxiv.org/abs/2306.02590
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, the finite orbits are confined to a curve. This goes in a similar direct
Externí odkaz:
http://arxiv.org/abs/2302.00859
We consider D-finite power series $f(z)=\sum a_n z^n$ with coefficients in a number field $K$. We show that there is a dichotomy governing the behaviour of $h(a_n)$ as a function of $n$, where $h$ is the absolute logarithmic Weil height. As an immedi
Externí odkaz:
http://arxiv.org/abs/2205.02145
We prove several results on backward orbits of rational functions over number fields. First, we show that if $K$ is a number field, $\phi\in K(x)$ and $\alpha\in K$ then the extension of $K$ generated by the abelian points in the backward orbit of $\
Externí odkaz:
http://arxiv.org/abs/2203.10034
We study the Betti map of a particular (but relevant) section of the family of Jacobians of hyperelliptic curves using the polynomial Pell equation $A^2-DB^2=1$, with $A,B,D\in \mathbb C[t]$ and certain ramified covers ${\mathbb P}^1\to {\mathbb P}^1
Externí odkaz:
http://arxiv.org/abs/2109.13552