2015/11/06 by Hanna, Gautier
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1511.02068
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.