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arXiv · 1105.3895

Prescribing the binary digits of primes

Jean Bourgain
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Abstract

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.

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Jean Bourgain. 2012-01-09. Prescribing the binary digits of primes. https://arxiv.org/abs/1105.3895

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