Let denote the polynomial ring over , the finite field of elements. Suppose the characteristic of is not or . We prove that there exist infinitely many such that the set contains a Sidon set which is an additive basis of order .
A combinatorial description of spectral isomorphisms between Morse flows is provided. We introduce the notion of a regular spectral isomorphism and we study some invariants of such isomorphisms. In the case of Morse cocycles taking values in , where p is a prime, each spectral isomorphism is regular. The same holds true for arbitrary finite abelian groups under an additional combinatorial condition of asymmetry in the defining Morse sequence, and for Morse flows of rank one. Rank one is shown to...
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.
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.
Démonstration élémentaire de la finitude de l’ensemble de type associé à une suite de densité uniforme extérieure non nulle.