Journal article
Quantitative bounds for Gowers uniformity of the Möbius and von Mangoldt functions
- Abstract:
- We establish quantitative bounds on the U k[N] Gowers norms of the M & ouml;bius function mu and the von Mangoldt function A for all k, with error terms of the shape O((log log N)-c). As a consequence, we obtain quantitative bounds for the number of solutions to any linear system of equations of finite complexity in the primes, with the same shape of error terms. We also obtain the first quantitative bounds on the size of sets containing no k-term arithmetic progressions with shifted prime difference
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 621.2KB, Terms of use)
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- Publisher copy:
- 10.4171/jems/1404
- Publication website:
- https://www.utupub.fi/bitstream/10024/190701/1/10.4171-jems-1404.pdf
Authors
- Publisher:
- EMS Press
- Journal:
- Journal of the European Mathematical Society More from this journal
- Volume:
- 27
- Issue:
- 4
- Pages:
- 1321-1384
- Publication date:
- 2023-12-12
- Acceptance date:
- 2023-10-10
- DOI:
- EISSN:
-
1435-9863
- ISSN:
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1435-9855
- Language:
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English
- Keywords:
- Pubs id:
-
1602920
- Local pid:
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pubs:1602920
- Source identifiers:
-
W4389618080
- Deposit date:
-
2026-06-05
- ARK identifier:
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Terms of use
- Copyright date:
- 2023
- Licence:
- CC Attribution (CC BY)
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