Completeness of the absolute Galois group of the rational number field.
2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.We call a complex (quasiprojective) surface of hyperbolic type, iff – after removing finitely many points and/or curves – the universal cover is the complex two-dimensional unit ball. We characterize abelian surfaces which have a birational transform of hyperbolic type by the existence of a reduced divisor with only elliptic curve components and maximal singularity rate (equal to 4). We discover a Picard modular surface of...
On calcule par des méthodes arithmétiques le groupe de Brauer non ramifié des espaces homogènes de groupes algébriques linéaires sur différents corps. Les formules obtenues font intervenir l’hypercohomologie de complexes de groupes de type multiplicatif.
La complexité d’une suite infinie est définie comme la fonction qui compte le nombre de facteurs de longueur dans cette suite. Nous prouvons ici que la complexité des suites de Rudin-Shapiro généralisées (qui comptent les occurrences de certains facteurs dans les développements binaires d’entiers) est ultimement affine.
The aim of this paper is to evaluate the growth order of the complexity function (in rectangles) for two-dimensional sequences generated by a linear cellular automaton with coefficients in , and polynomial initial condition. We prove that the complexity function is quadratic when l is a prime and that it increases with respect to the number of distinct prime factors of l.
Let be an ergodic translation on the compact group and a continuity set, i.e. a subset with topological boundary of Haar measure 0. An infinite binary sequence defined by if and otherwise, is called a Hartman sequence. This paper studies the growth rate of , where denotes the number of binary words of length occurring in . The growth rate is always subexponential and this result is optimal. If is an ergodic translation
We study the complexity of the infinite word associated with the Rényi expansion of in an irrational base . When is the golden ratio, this is the well known Fibonacci word, which is sturmian, and of complexity . For such that is finite we provide a simple description of the structure of special factors of the word . When we show that . In the cases when or we show that the first difference of the complexity function takes value in for every , and consequently we determine...
We study the complexity of the infinite word uβ associated with the Rényi expansion of 1 in an irrational base β > 1. When β is the golden ratio, this is the well known Fibonacci word, which is Sturmian, and of complexity C(n) = n + 1. For β such that dβ(1) = t1t2...tm is finite we provide a simple description of the structure of special factors of the word uβ. When tm=1 we show that C(n) = (m - 1)n + 1. In the cases when t1 = t2 = ... tm-1or t1 > max{t2,...,tm-1} we show that the first difference of...
Le terme principal de la moyenne, sur les discriminants quadratiques satisfaisant la condition de Heegner, de la hauteur de Néron-Tate des points de Heegner d’une courbe elliptique rationnelle a été déterminé dans [13]. Les auteurs ont également conjecturé l’expression du terme suivant. Dans cet article, il est démontré que cette expression est correcte et une asymptotique précise, qui sauve une puissance dans le terme d’erreur, est obtenue. Les annulations des coefficients de Fourier de formes...