Related papers: Computing algebraic numbers of bounded height
We study the set of algebraic numbers of bounded height and bounded degree where an analytic transcendental function takes algebraic values.
We prove that the height of any algebraic computation tree for deciding membership in a semialgebraic set is bounded from below (up to a multiplicative constant) by the logarithm of m-th Betti number (with respect to singular homology) of…
We propose a method for computing upper bounds for the Heilbronn problem for triangles.
We prove an asymptotic formula for the number of multi-quadratic number fields of bounded discriminant with a power-saving error term. Furthermore, we explicitly calculate the leading coefficient and extend our result to totally real…
We propose an algorithm for classification of linear codes over different finite fields based on canonical augmentation. We apply this algorithm to obtain classification results over fields with 2, 3 and 4 elements.
We present an algorithm that, on input $n$, lists every unlabeled tree of order $n$.
The aim of this paper is to show that there exists a deterministic algorithm that can be applied to compute the factors of a polynomial of degree 2, defined over a finite field, given certain conditions.
Let $F$ be a univariate polynomial or rational fraction of degree $d$ defined over a number field. We give bounds from above on the absolute logarithmic Weil height of $F$ in terms of the heights of its values at small integers: we review…
Given a set of endomorphisms on $\mathbb{P}^N$, we establish an upper bound on the number of points of bounded height in the associated monoid orbits. Moreover, we give a more refined estimate with an associated lower bound when the monoid…
Let $k$ be a finite field extension of the function field $\bfF_p(T)$ and $\bar{k}$ its algebraic closure. We count points in projective space $\Bbb P ^{n-1}(\bar{k})$ with given height and of fixed degree $d$ over the field $k$. If…
We show that the height of a variety over a finitely generated field of characteristic zero can be written as an integral of local heights over the set of places of the field. This allows us to apply our previous work on toric varieties and…
We establish asymptotic formulas for the number of integral points of bounded height on toric varieties.
We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we…
In this paper we prove a formula for the number of rational points of bounded height relative to all the generators of the cone of effective divisor for a toric variety over a number field.
In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.
An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit…
Inspired by previous work of Shoup, Lenstra-De Smit and Couveignes-Lercier, we give fast algorithms to compute in (the first levels of) the ell-adic closure of a finite field. In many cases, our algorithms have quasi-linear complexity.
We give upper and lower bounds on the Chevalley-Bass number of a field of characteristic zero, whenever this quantity is well-defined. We also describe an algorithm which computes the Chevalley-Bass number of a field, provided its maximal…
We give an efficient algorithm to enumerate all sets of $r\ge 1$ quadratic polynomials over a finite field, which remain irreducible under iterations and compositions.
In the paper we partially solved the problem of the distribution of the discriminants of integral polynomials in the cubic case. We proved the asymptotic formula for the number of integral cubic polynomials having bounded height and bounded…