Polynômes trigonométriques et marches aléatoires multidimensionnelles : application à la théorie ergodique
Une remarque sur un théorème de Bourgain
The mantissa distribution of the primorial numbers
We show that the sequence of mantissas of the primorial numbers Pₙ, defined as the product of the first n prime numbers, is distributed following Benford's law. This is done by proving that the values of the first Chebyshev function at prime numbers are uniformly distributed modulo 1. We provide a convergence rate estimate. We also briefly treat some other sequences defined in the same way as Pₙ.
Théorèmes ergodiques multidimensionnels et suites aléatoires universellement représentatives en moyenne
Sur une inégalité de Littlewood-Salem
Ergodic averages with deterministic weights
We study the convergence of the ergodic averages where is a bounded sequence and a strictly increasing sequence of integers such that for some . Moreover we give explicit such sequences and and we investigate in particular the case where is a -multiplicative sequence.
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