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On the Brun-Titchmarsh theorem

Abstract:

The Brun–Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(ϕ(q)logx) for some value C depending on logx/logq. Different authors have provided different estimates for C in different ranges for logx/logq, all of which give C>2 when logx/logq is bounded. We show that one can take C=2 provided that logx/logq≥8 and q is sufficiently large. Moreover, we also produce a lower bound of size x/(q1/2ϕ(q)) when logx/logq≥8 and ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Author's Original

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Publisher copy:
10.4064/aa157-3-3

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Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
Publisher:
Polskiej Akademii Nauk, Instytut Matematyczny Publisher's website
Journal:
Acta Arithmetica Journal website
Volume:
157
Pages:
249-296
Publication date:
2013-01-01
DOI:
ISSN:
0065-1036 and 1730-6264
Pubs id:
pubs:404764
URN:
uri:f34a2af4-c36d-4f9b-bad7-016a7a989203
UUID:
uuid:f34a2af4-c36d-4f9b-bad7-016a7a989203
Local pid:
pubs:404764

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