- Abstract:
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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 ...
Expand abstract - Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Author's Original
- Files:
-
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(pdf, 465.5KB)
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- Publisher copy:
- 10.4064/aa157-3-3
-
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- 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:
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0065-1036 and 1730-6264
- Pubs id:
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pubs:404764
- URN:
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uri:f34a2af4-c36d-4f9b-bad7-016a7a989203
- UUID:
-
uuid:f34a2af4-c36d-4f9b-bad7-016a7a989203
- Local pid:
- pubs:404764
- Copyright holder:
- Instytut Matematyczny PAN
- Copyright date:
- 2013
- Notes:
- This is a pre-print version of a journal article published by Instytut Matematyczny in Acta Arithmetica in 2013, available online: http://dx.doi.org/10.4064/aa157-3-3
Journal article
On the Brun-Titchmarsh theorem
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