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Exponential sums with automatic sequences

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arxiv 1710.01091 v1 pith:OVQCUWBX submitted 2017-10-03 math.NT

Sary Drappeau , Clemens Müllner This is my paper · ORCID
classification math.NT
keywords automaticsequencessumsappliesasymptoticallyboundedcongruenceconsequence
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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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  1. The Prime Digit Distribution Conjecture: A Formal Proof of Average Digit Equidistribution in the Prime Numbers

    math.NT 2026-07 conditional novelty 5.0 of 10

    Pooled over all positions and all primes below 10^n, each decimal digit occurs with frequency 1/10 + O((log n)/n).

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