Published March 2022
| Accepted Version
Journal Article
Open
Fractional Parts of Non-Integer Powers of Primes. II
- Creators
- Shubin, Andrei
Abstract
We continue to study the distribution of prime numbers p, satisfying the condition {p^α} ∈ I ⊂ [0;1), in arithmetic progressions. In the paper, we prove an analogue of Bombieri-Vinogradov theorem for 0 < α < 1/9 with the level of distribution θ = 2/5 − (3/5)α, which improves the previous result corresponding to θ ≤ 1/3.
Additional Information
© The Author(s) 2021. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) Received: 24 November 2020. Revision received: 26 May 2021. Accepted: 11 June 2021. Corrected and typeset: 28 June 2021. Published: 28 June 2021. I would like to thank M. A. Korolev and M. Radziwill for many helpful discussions and advice. I also thank the anonymous referee for the careful reading of the paper and for pointing out a mistake in the earlier version.Attached Files
Accepted Version - 2011.11790.pdf
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2011.11790.pdf
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- Eprint ID
- 114006
- Resolver ID
- CaltechAUTHORS:20220322-742376000
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2022-03-23Created from EPrint's datestamp field
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2022-03-23Created from EPrint's last_modified field