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Primes with restricted digits

Abstract:

Let a0 ∈ {0,…,9}. We show there are infinitely many prime numbers which do not have the digit a0 in their decimal expansion. The proof is an application of the Hardy–Littlewood circle method to a binary problem, and rests on obtaining suitable ‘Type I’ and ‘Type II’ arithmetic information for use in Harman’s sieve to control the minor arcs. This is obtained by decorrelating Diophantine conditions which dictate when the Fourier transform of the primes is large from digital conditions which dic...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

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Publisher copy:
10.1007/s00222-019-00865-6

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Magdalen College
ORCID:
0000-0001-5782-7082
Publisher:
Springer Berlin Heidelberg Publisher's website
Journal:
Inventiones Mathematicae Journal website
Volume:
217
Issue:
1
Pages:
127–218
Publication date:
2019-03-04
Acceptance date:
2019-02-07
DOI:
EISSN:
1432-1297
ISSN:
0020-9910
Pubs id:
pubs:969438
URN:
uri:96ca35bb-1b31-42a9-a21e-c11790f0f642
UUID:
uuid:96ca35bb-1b31-42a9-a21e-c11790f0f642
Local pid:
pubs:969438

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