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La somme des chiffres des carrés

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Acta Mathematica

Résumé

L’objet de cet article est de répondre à une question posée par Gelfond en 1968 en montrant que la somme des chiffres des carrés écrits en base q ⩾ 2 est équirépartie dans les progressions arithmétiques.

Abstract

In this article we answer a question proposed by Gelfond in 1968. We prove that the sum of digits of squares written in a basis q ⩾ 2 is equidistributed in arithmetic progressions.

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Authors and Affiliations

  1. Institut de Mathématiques de Luminy CNRS-UMR 6206, 163 avenue de Luminy, Case 907, FR-13288, Marseille Cedex 9, France

    Christian Mauduit & Joël Rivat

Authors
  1. Christian Mauduit
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  2. Joël Rivat
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Correspondence to Joël Rivat.

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Mauduit, C., Rivat, J. La somme des chiffres des carrés. Acta Math 203, 107–148 (2009). https://doi.org/10.1007/s11511-009-0040-0

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  • DOI: https://doi.org/10.1007/s11511-009-0040-0

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