Sur les occurrences des mots dans les nombres premiers
Volume 178 / 2017
Acta Arithmetica 178 (2017), 15-42
MSC: Primary 11A63; Secondary 11B85, 11N05, 11L20.
DOI: 10.4064/aa8337-8-2016
Published online: 5 January 2017
Abstract
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 block-additive sequences on finite and infinite expansions. We also give a partial answer to a question posed by Kalai.
