麻豆AV

On prime numbers with as many ones as zeros in their binary expansion.

Drmota, Mauduit and Rivat showed in 2009 that the set $E$ of prime numbers with as many ones as zeros in their binary expansion is infinite (they actually gave an asymptotic formula for $sharp E cap [1,N]$ for $N>2$). We prove that for every irrational number $eta$, the sequence $(eta p)_{pin E}$ is uniformly distributed modulo 1. This is a joint work with Christian Mauduit and Jo毛l Rivat (Universit茅 d鈥橝ix-Marseille).