Test for submodel in Gibbs-Markov binary random sequence
The distribution of Farey points, I
The distribution of inverses modulo a prime in short intervals
The Erdős and Halberstam theorems for Drinfeld modules of any rank (with an appendix by Hugh Thomas)
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.
The relative size of consecutive odd denominators in Farey series.
Tijdeman's Iterative Algorithm
Two random constructions inside lacunary sets
We study the relationship between the growth rate of an integer sequence and harmonic and functional properties of the corresponding sequence of characters. In particular we show that every polynomial sequence contains a set that is for all but is not a Rosenthal set. This holds also for the sequence of primes.