2011/05/19 by Jean Bourgain, Bourgain, Jean
Mathematics · #11N05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11N05
paper · pdf · doi:10.48550/arxiv.1105.3895
22 pages
arxiv created 2012/01/09 · arxiv updated 2012/01/10
We present a new result on counting primes p<N=2n 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(\frac nlog n)4/7. This condition results from the estimates of Gallagher and Iwaniec on zero-free regions of L-functions with `powerful' conductor.