A new lower bound for
We prove that, for all integers exceeding some effectively computable number , the distance from to the nearest integer is greater than .
A note on irregularities in distribution of sequences of integers
A note on the lonely runner conjecture.
A problem of Erdős-Szüsz-Turán on diophantine approximation
A remark on a theorem of L. Carlitz
A Sequence Has Almost Nowhere Small Discrepancy.
A survey of results on density modulo of double sequences containing algebraic numbers
In this survey article we start from the famous Furstenberg theorem on non-lacunary semigroups of integers, and next we present its generalizations and some related results.
Actions of sets of integers on irrationals
Addendum to “On the problem”
Approximations diophantiennes asymptotiques.
Automates finis et ensembles normaux
Soit une suite strictement croissante d’entiers reconnaissable par un automate fini. Nous montrons qu’une condition nécessaire et suffisante pour que l’ensemble normal associé a soit exactement est que l’un au moins des sommets qui reconnaît la suite soit précédé dans le graphe de l’automate par un sommet possédant au moins deux circuits fermés distincts. Cette condition peut se traduire quantitativement en disant que la suite doit être plus “dense” que toute suite exponentielle.
Averages of short exponential sums
Billiards and the five distance theorem
Bounded discrepancy sets
-uniform distribution of entire functions
Calculation of improper integrals using uniformly distributed sequences
Characterizations of groups generated by Kronecker sets
In recent years, starting with the paper [B-D-S], we have investigated the possibility of characterizing countable subgroups of the torus by subsets of . Here we consider new types of subgroups: let be a Kronecker set (a compact set on which every continuous function can be uniformly approximated by characters of ), and the group generated by . We prove (Theorem 1) that can be characterized by a subset of (instead of a subset of ). If is finite, Theorem 1 implies our earlier result...
Comments on the fractional parts of Pisot numbers
Let be the set of limit points of the fractional parts , , where is a Pisot number and . Using a description of , due to Dubickas, we show that there is a sequence of elements of such that , . Also, we prove that the...
Conditions suffisantes d’équirépartition modulo 1 de suites et
Conditions suffisantes d'équirépartition modulo 1 . Problème de Waring-Golbach pour f (x) == Xc , c non entier.