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Théorème des nombres premiers pour les fonctions digitales

Volume 165 / 2014

Bruno Martin, Christian Mauduit, Joël Rivat Acta Arithmetica 165 (2014), 11-45 MSC: 11A41, 11A63, 11L20. DOI: 10.4064/aa165-1-2

Abstract

The aim of this work is to estimate exponential sums of the form $ \sum _{n\le x} \varLambda (n) \exp(2i\pi (f(n)+\beta n)), $ where $\varLambda $ denotes von Mangoldt's function, $f$ a digital function, and $\beta \in \mathbb {R}$ a parameter. This result can be interpreted as a Prime Number Theorem for rotations (i.e. a Vinogradov type theorem) twisted by digital functions.

Authors

  • Bruno MartinLaboratoire de Mathématiques
    Pures et Appliquées Joseph Liouville
    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 MauduitInstitut de Mathématiques de Marseille
    UMR 7373 CNRS
    Université d'Aix-Marseille
    163 avenue de Luminy, Case 907
    13288 Marseille Cedex 9, France
    and
    IMPA–CNRS, UMI 2924
    Instituto de Matemática
    Pura e Aplicada
    Estrada Dona Castorina 110
    22460-320 Rio de Janeiro, Brasil
    e-mail
  • Joël RivatInstitut de Mathématiques de Marseille
    UMR 7373 CNRS
    Université d'Aix-Marseille
    163 avenue de Luminy, Case 907
    13288 Marseille Cedex 9, France
    e-mail

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