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Fonctions digitales le long des nombres premiers

Volume 170 / 2015

Bruno Martin, Christian Mauduit, Joël Rivat Acta Arithmetica 170 (2015), 175-197 MSC: 11A63, 11B85, 11N05. DOI: 10.4064/aa170-2-5

Abstract

In a recent work we gave some estimations for exponential sums of the form $\sum_{n\le x} \varLambda(n) \exp(2i\pi (f(n) + \beta n)), $ where $\varLambda$ denotes the von Mangoldt function, $f$ a digital function, and $\beta$ 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.

Authors

  • Bruno MartinLMPA, Centre Universitaire de la Mi-Voix
    Maison de la Recherche Blaise Pascal
    50 rue F. Buisson, B.P. 699
    62228 Calais Cedex, France
    e-mail
  • Christian MauduitUniversité d'Aix-Marseille
    et Institut Universitaire de France
    Institut de Mathématiques de Marseille
    CNRS UMR 7373
    163 avenue de Luminy, Case 907
    13288 Marseille Cedex 9, France
    e-mail
  • Joël RivatUniversité d'Aix-Marseille
    Institut de Mathématiques de Marseille
    CNRS UMR 7373
    163 avenue de Luminy, Case 907
    13288 Marseille Cedex 9, France
    e-mail

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