Prescribing the binary digits of primes
Abstract
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( n n)4/7. This condition results from the estimates of Gallagher and Iwaniec on zero-free regions of L-functions with `powerful' conductor.
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