论文标题
在原理字段中，素数的thue-morse和Rudin-shapiro序列
The Thue-Morse and Rudin-Shapiro sequences at primes in principal number fields
论文作者
论文摘要
我们在整数中考虑一个数字系统$ {\ MATHCAL O} _K $的数字字段，我们假设是主要字段。我们证明，$ {\ mathcal o} _k $中素数的属性是从相对于所选的计算系统的两个自动序列的两个基本示例（thue-morse和rudin-shapiro序列）解释的。这是一个类似物，以$ {\ mathcal o} _k $为单位，是莫杜特 - 里瓦特（Mauduit-rivat）的结果，与情况有关，涉及$ k = {\ mathbb q} $。
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 $K={\mathbb Q}$.
