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  • [hal-00904678] A dynamical point of view on the set of B-free integers

    15 novembre 2017, par El Houcein El Abdalaoui, Mariusz Lemanczyk, Thierry De La Rue
    We extend the study of the square-free flow, recently introduced by Sarnak, to the more general context of B-free integers, that is to say integers with no factor in a given family B of pairwise relatively prime integers, the sum of whose reciprocals is finite. Relying on dynamical arguments, (...)
  • [hal-01070531] The Chowla and the Sarnak conjectures from ergodic theory point of view

    15 novembre 2017, par El Houcein El Abdalaoui, Joanna Kulaga-Przymus, Mariusz Lemanczyk, Thierry De La Rue
    We rephrase the conditions from the Chowla and the Sarnak conjectures in abstract setting, that is, for sequences of numbers in -1,0,1, and introduce several natural generalizations. We study the relationships between these properties and other notions from topological dynamics and ergodic (...)
  • [hal-00574623] Averaging along Uniform Random Integers

    15 novembre 2017, par Élise Janvresse, Thierry De La Rue
    Motivated by giving a meaning to ''The probability that a random integer has initial digit d'', we define a URI-set as a random set E of natural integers such that each n>0 belongs to E with probability 1/n, independently of other integers. This enables us to introduce two notions of (...)
  • [hal-01499011] A note on some constants related to the zeta–function and their relationship with the Gregory coefficients

    15 novembre 2017, par Iaroslav Blagouchine, Marc-Antoine Coppo
    In this article, new series for the first and second Stieltjes constants (also known as generalized Eu-ler's constant), as well as for some closely related constants are obtained. These series contain rational terms only and involve the so–called Gregory coefficients, which are also known as (...)
  • [hal-00767319] Points rationnels de la fonction Gamma d’Euler

    14 novembre 2017, par Etienne Besson
    We use a method, first developed for the Riemann zeta-function by Masser in ["Rational values of the Riemann zeta function", Journ. Num. Th. 131 (2011), 2037-2046], to prove a new zero estimate for polynomials in z and 1/Gamma(z). This allows us to prove that, for all n>=2, there (...)

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