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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Rudin-Shapiro sequences along squares


Authors: Christian Mauduit and Joël Rivat
Journal: Trans. Amer. Math. Soc. 370 (2018), 7899-7921
MSC (2010): Primary 11A63, 11B85, 11J71, 37A45
DOI: https://doi.org/10.1090/tran/7210
Published electronically: May 9, 2018
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Abstract: We estimate exponential sums of the form $ \sum _{n\leq x} f(n^2) \mathrm {e}(\vartheta n)$ for a large class of digital functions $ f$ and $ \vartheta \in \mathbb{R}$. We deduce from these estimates the distribution along squares of this class of digital functions which includes the Rudin-Shapiro sequence and some of its generalizations.


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Christian Mauduit
Affiliation: Université d’Aix-Marseille et Institut Universitaire de France, Institut de Mathématiques de Marseille, CNRS UMR 7373, Case 907, 163, avenue de Luminy, 13288 MARSEILLE Cedex 9, France
Email: mauduit@iml.univ-mrs.fr

Joël Rivat
Affiliation: Université d’Aix-Marseille, Institut de Mathématiques de Marseille, CNRS UMR 7373, Case 907, 163, avenue de Luminy, 13288 MARSEILLE Cedex 9, France
Email: joel.rivat@univ-amu.fr

DOI: https://doi.org/10.1090/tran/7210
Keywords: Rudin--Shapiro sequences, exponential sums
Received by editor(s): December 3, 2015
Received by editor(s) in revised form: February 16, 2017
Published electronically: May 9, 2018
Additional Notes: This work was supported by the Agence Nationale de la Recherche project ANR-14-CE34-0009 MUDERA and Ciência sem Fronteiras, projet PVE 407308/2013-0
Article copyright: © Copyright 2018 American Mathematical Society

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