Rudin–Shapiro sequences along squares
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- by Christian Mauduit and Joël Rivat PDF
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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.References
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Additional Information
- 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
- MR Author ID: 207610
- 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
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 7899-7921
- MSC (2010): Primary 11A63, 11B85, 11J71, 37A45
- DOI: https://doi.org/10.1090/tran/7210
- MathSciNet review: 3852452