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On the correlation of the sum of digits along prime numbers

Volume 199 / 2021

Karam Aloui, Christian Mauduit, Mohamed Mkaouar Acta Arithmetica 199 (2021), 275-301 MSC: Primary 11A07, 11A41, 11A63, 11L07, 11L20; Secondary 11B50, 11L03, 11N13. DOI: 10.4064/aa200514-22-12 Published online: 19 April 2021

Abstract

Let $s_{q}$ denote the sum of digits function in base $q$. The aim of this work is to estimate the exponential sums involving the sum of digits of shifted prime numbers, of the form $\sum _{p\leq x}e(\alpha _{0}s_{q}(p)+\cdots +\alpha _{k}s_{q}(p+k))$, where $k$ is a positive integer and $\alpha _{0},\ldots ,\alpha _{k}$ are real numbers. We deduce from these estimates some results concerning the correlation along prime numbers of the Thue–Morse sequence.

Authors

  • Karam AlouiTechnische Universität Wien
    E104 – Institut für Diskrete Mathematik
    und Geometrie
    Wiedner Hauptstr. 8
    1040 Wien, Österreich
    and
    Université de Sfax
    Faculté des Sciences de Sfax
    Route Soukra, B.P. 1171
    Sfax 3000, Tunisie
    e-mail
  • Christian MauduitUniversité d’Aix-Marseille
    and Institut Universitaire de France
    Institut de Mathématiques
    de Marseille UMR 7373 CNRS
    Campus de Luminy, case 907
    13288 Marseille Cedex 9, France
    e-mail
  • Mohamed MkaouarUniversité de Sfax
    Faculté des Sciences de Sfax
    Route Soukra, B.P. 1171
    Sfax 3000, Tunisie
    e-mail

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