arXiv subjects

Gautier Hanna

Publications and source records attributed to Gautier Hanna.

3 recordsLinked to original sources

arXiv2020

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

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 $K={\mathbb Q}$.

math.NT↗

arXiv2016

Blocs de chiffres de taille croissante dans les nombres premiers

In this article, we prove a theorem à la Mauduit et Rivat (prime number theorem, Moebius randomness principle) for functions that count digital blocks whose length is a growing function tending to infinity. These sequences are not automatic. To obtain our results, we control sums of type I and II and use an adapted and refined version of the carry propagation property as well as standard methods from harmonic analysis.

math.NT↗

arXiv2015

Sur les occurrences des mots dans les nombres premiers

In this paper, we generalize Mauduit and Rivat's theorem on the Rudin-Shapiro sequence. Weakening the hypothesis needed in their theorem, we prove a prime number theorem for a large class of functions defined on the digits. Our result covers the case of generalized Rudin-Shapiro sequences as well as bloc-additive sequences on finite and infinite expansions. We also give a partial answer to a question posed by Kalai.

math.NT↗