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Prescribing the binary digits of primes

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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/log 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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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Jean Bourgain

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  1. Jean Bourgain
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Correspondence to Jean Bourgain.

Additional information

This research was partially supported by NSF grants DMS-0808042 and DMS-0835373.

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Bourgain, J. Prescribing the binary digits of primes. Isr. J. Math. 194, 935–955 (2013). https://doi.org/10.1007/s11856-012-0104-2

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  • DOI: https://doi.org/10.1007/s11856-012-0104-2

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