Rudin--Shapiro sequences along squares

Rudin--Shapiro sequences along squares

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 a...

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Veröffentlicht in:Transactions of the American Mathematical Society 2018-11, Vol.370 (11), p.7899-7921
Hauptverfasser: MAUDUIT, CHRISTIAN, RIVAT, JOËL
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Number Theory
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Zusammenfassung: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.
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/7210