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Primes represented by incomplete norm forms

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 wh...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1017/fmp.2019.8

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Magdalen College
Role:
Author
ORCID:
0000-0001-5782-7082
Publisher:
Cambridge University Press Publisher's website
Journal:
Forum of Mathematics, Pi Journal website
Volume:
8
Issue:
2020
Article number:
e3
Publication date:
2020-02-06
Acceptance date:
2019-11-17
DOI:
ISSN:
2050-5086
Source identifiers:
1074359
Pubs id:
pubs:1074359
UUID:
uuid:398d0ea7-6e21-44a6-82fa-112477ca47d2
Local pid:
pubs:1074359
Deposit date:
2019-11-26

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