Exponential sums with automatic sequences Article Swipe
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Sary Drappeau
,
Clemens Müllner
·
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.4064/aa171002-20-3
· OA: W2764047583
YOU?
·
· 2018
· Open Access
·
· DOI: https://doi.org/10.4064/aa171002-20-3
· OA: W2764047583
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 Pólya-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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