Journal article

### 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 ...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Author's original, pdf, 465.5KB)
Publisher copy:
10.4064/aa157-3-3

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
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:
1730-6264 and 0065-1036
Keywords:
Pubs id:
pubs:404764
UUID:
Local pid:
pubs:404764
Deposit date:
2016-10-17