%0 Journal Article
%T Prescribing the binary digits of primes
%A Jean Bourgain
%J Mathematics
%D 2011
%I arXiv
%X We present a new result on counting primes $p<N=2^n$ for which $r$ (arbitrarily placed) digits in the binary expansion of $p$ are specified. Compared with earlier work of Harman and Katai, the restriction on $r$ is relaxed to $r< c\Big(\frac n{\log n}\Big)^{4/7}$. This condition results from the estimates of Gallagher and Iwaniec on zero-free regions of $L$-functions with `powerful' conductor.
%U http://arxiv.org/abs/1105.3895v2