Rudin–Shapiro sequences along squares

Abstract : We estimate exponential sums of the form Sigma(n <= x) f(n(2)) e(nu n) for a large class of digital functions f and nu is an element of 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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https://hal.archives-ouvertes.fr/hal-02075857
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Submitted on : Thursday, March 21, 2019 - 4:18:08 PM
Last modification on : Friday, March 22, 2019 - 1:25:39 AM

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Christian Mauduit, Joel Rivat. Rudin–Shapiro sequences along squares. Transactions of the American Mathematical Society, American Mathematical Society, 2018, 370 (11), pp.7899-7921. ⟨10.1090/tran/7210⟩. ⟨hal-02075857⟩

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