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arXiv · 2001.07017

The Thue-Morse and Rudin-Shapiro sequences at primes in principal number fields

Sary Drappeau·Gautier Hanna
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Abstract

We consider a numeration system in the ring of integers ${\mathcal O}_K$ of a number field, which we assume to be principal. We prove that the property of being a prime in ${\mathcal O}_K$ is decorrelated from two fundamental examples of automatic sequences relative to the chosen numeration system: the Thue-Morse and the Rudin-Shapiro sequences. This is an analogue, in ${\mathcal O}_K$, of results of Mauduit-Rivat which were concerned with the case $K={\mathbb Q}$.

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Sary Drappeau, Gautier Hanna. 2020-01-20. The Thue-Morse and Rudin-Shapiro sequences at primes in principal number fields. https://doi.org/10.1007/s10474-020-01030-9

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