Rudin–Shapiro sequences along squares

Mauduit, Christian; Rivat, Joël

doi:10.1090/tran/7210

Rudin–Shapiro sequences along squares
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by Christian Mauduit and Joël Rivat PDF

Trans. Amer. Math. Soc. 370 (2018), 7899-7921 Request permission

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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