%0 Journal Article %T Prime numbers along Rudin–Shapiro sequences %+ Institut de Mathématiques de Marseille (I2M) %A Mauduit, Christian %A Rivat, Joël %< avec comité de lecture %@ 1435-9855 %J Journal of the European Mathematical Society %I European Mathematical Society %V 17 %N 10 %P 2595–2642 %8 2015 %D 2015 %R 10.4171/JEMS/566 %K Rudin–Shapiro sequence %K prime numbers %K Möbius function %K exponential sums %Z Mathematics [math]/Number Theory [math.NT]Journal articles %X For a large class of digital functions f, we estimate the sums Sigma(n <= x) Lambda(n)f (n) (and Sigma(n <= x) mu(n)f (n)), where Lambda denotes the von Mangoldt function (and mu, the Mobius function). We deduce from these estimates a Prime Number Theorem (and a Mobius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations. %G English %L hal-01259940 %U https://hal.science/hal-01259940 %~ CNRS %~ UNIV-AMU %~ EC-MARSEILLE %~ INSMI %~ I2M %~ I2M-2014- %~ ANR