Exponential sums with automatic sequences

Sary Drappeau; Clemens Müllner

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arXiv · 1710.01091

Exponential sums with automatic sequences

Sary Drappeau·Clemens Müllner

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Abstract

We show that automatic sequences are asymptotically orthogonal to periodic exponentials of type $e_q(f(n))$, where $f$ is a rational fraction, in the P\'olya-Vinogradov range. This applies to Kloosterman sums, and may be used to study solubility of congruence equations over automatic sequences. We obtain this as consequence of a general result, stating that sums over automatic sequences can be bounded effectively in terms of two-point correlation sums over intervals.

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Sary Drappeau, Clemens Müllner. 2017-10-03. Exponential sums with automatic sequences. https://arxiv.org/abs/1710.01091

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