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Sur certaines équations fonctionnelles approchées, liées à la transformation de Gauss

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Abstract

In line with classical work by Hardy, Littlewood and Wilton, we study a class of functional equations involving the Gauss transformation from the theory of continued fractions. This allows us to reprove, among others, a convergence criterion for a diophantine series considered by Chowla, and to give additional information about the sum of this series.

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Acknowledgements

Outre leurs laboratoires respectifs, les auteurs remercient les UMI 2615 (CNRS-UIM, Moscou) et 3457 (CNRS-CRM, Montréal), qui ont fourni des conditions idéales pour leur travail sur cet article.

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Authors and Affiliations

  1. Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France

    Michel Balazard

  2. ULCO, LMPA, Calais, France

    Bruno Martin

Authors
  1. Michel Balazard
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  2. Bruno Martin
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Correspondence to Michel Balazard.

Additional information

Bruno Martin is supported by ANR Grant MUDERA ANR-14-CE34-0009.

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Balazard, M., Martin, B. Sur certaines équations fonctionnelles approchées, liées à la transformation de Gauss. Aequat. Math. 93, 563–585 (2019). https://doi.org/10.1007/s00010-018-0594-z

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  • DOI: https://doi.org/10.1007/s00010-018-0594-z

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