An improved estimate on the distribution mod 1 of powers of real matrices
An improved result on irregularities in distribution of sequences of integers
In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.
An improved upper bound for the discrepancy of quadratic congruential pseudorandom numbers
An iterated logarithm type theorem for the largest coefficient in continued fractions
An L¹ estimate for half-space discrepancy
Application de la théorie des algèbres de mesures à l'étude des mesures spectrales.
Application of the circle method on multidimensional limit-periodic functions
Applications de la notion d'entropie au développement d'un nombre réel dans une base de Pisot
Soit un nombre de Pisot de degré ; nous avons montré précédemment que l’endomorphisme du tore dont est valeur propre est facteur du -shift bilatéral par une application continue ; nous prouvons ici (théorème 1) que l’application conserve l’entropie de toute mesure invariante sur le -shift. Ceci permet de définir l’entropie d’un nombre dans la base et d’en étudier la stabilité. Nous généralisons également des résultats de Kamae, Rauzy et Bernay.
Approximate squaring.
Approximations diophantiennes asymptotiques.
Approximations diophantiennes dans un corps local
Approximations diophantiennes et eutaxie
Approximations diophantiennes et problèmes additifs dans les groupes abéliens localement compacts
Arithmetic and ergodic properties of 'flipped' continued fraction algorithms
Arithmetic functions on Beatty sequences
Arithmetic progressions of length three in subsets of a random set
Arithmetic progressions, prime numbers, and squarefree integers
In this paper we establish the distribution of prime numbers in a given arithmetic progression for which is squarefree.
Arithmetics in numeration systems with negative quadratic base
We consider positional numeration system with negative base , as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when is a quadratic Pisot number. We study a class of roots of polynomials , , and show that in this case the set of finite -expansions is closed under addition, although it is not closed under subtraction. A particular example is , the golden ratio. For such , we determine the exact bound on the number of fractional digits...
Asimptotic Distribution and Weak Convergence on Compact Riemannian Manifolds.
Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations