Geodesic
Exponential sums with automatic sequences
Sary Drappeau1 ; Clemens Müllner2
1 Aix Marseille Université CNRS, Centrale Marseille I2M UMR 7373 13453 Marseille, France
2 Institut für Diskrete Mathematik und Geometrie TU Wien Wiedner Hauptstr. 8–10 1040 Wien, Austria
Acta Arithmetica, Tome 185 (2018) no. 1, pp. 81-99 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that automatic sequences are asymptotically orthogonal to periodic exponentials of type~${\rm e}_q(f(n))$, 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.
DOI : 10.4064/aa171002-20-3
Keywords: automatic sequences asymptotically orthogonal periodic exponentials type where rational fraction lya vinogradov range applies kloosterman sums may study solubility congruence equations automatic sequences obtain consequence general result stating sums automatic sequences bounded effectively terms two point correlation sums intervals

Sary Drappeau 1 ; Clemens Müllner 2

1 Aix Marseille Université CNRS, Centrale Marseille I2M UMR 7373 13453 Marseille, France
2 Institut für Diskrete Mathematik und Geometrie TU Wien Wiedner Hauptstr. 8–10 1040 Wien, Austria 
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Sary Drappeau; Clemens Müllner. Exponential sums with automatic sequences. Acta Arithmetica, Tome 185 (2018) no. 1, pp. 81-99. doi: 10.4064/aa171002-20-3

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