On the metric theory of continued fractions
On Gelfond’s conjecture about the sum of digits of prime numbers
The goal of this paper is to outline the proof of a conjecture of Gelfond [] (1968) in a recent work in collaboration with Christian Mauduit [] concerning the sum of digits of prime numbers, reflecting the lecture given in Edinburgh at the Journées Arithmétiques 2007.
Répartition des fonctions q-multiplicatives dans la suite , c > 1
A Turán-Kubilius type inequality on sum sets
Propriétés q-multiplicatives de la suite , c > 1
Prime numbers along Rudin–Shapiro sequences
For a large class of digital functions , we estimate the sums (and , where denotes the von Mangoldt function (and the Möbius function). We deduce from these estimates a Prime Number Theorem (and a Möbius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations.
Fonctions digitales le long des nombres premiers
In a recent work we gave some estimations for exponential sums of the form , where Λ denotes the von Mangoldt function, f a digital function, and β a real parameter. The aim of this work is to show how these results can be used to study the statistical properties of digital functions along prime numbers.
Théorème des nombres premiers pour les fonctions digitales
The aim of this work is to estimate exponential sums of the form , where Λ denotes von Mangoldt’s function, f a digital function, and β ∈ ℝ a parameter. This result can be interpreted as a Prime Number Theorem for rotations (i.e. a Vinogradov type theorem) twisted by digital functions.
Pseudorandom sequences of binary vectors
On finite pseudorandom binary sequences IV: The Liouville function, II
On finite pseudorandom binary sequences III: The Liouville function, I
Computing the summation of the Möbius function.
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