Journal article
Ranges of polynomials control degree ranks of Green and Tao over finite prime fields
- Abstract:
- Let be a prime, let be integers, and let be a non-empty subset of . We establish that if a polynomial with degree is such that the image does not contain the full image of any non-constant polynomial with degree at most , then coincides on with a polynomial that in particular has bounded degree- -rank in the sense of Green and Tao. Similarly, we prove that if the assumption holds even for , then coincides on with a polynomial determined by a bounded number of coordinates.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 527.6KB, Terms of use)
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- Publisher copy:
- 10.1017/s0013091526101382
Authors
- Publisher:
- Cambridge University Press
- Journal:
- Proceedings of the Edinburgh Mathematical Society More from this journal
- Pages:
- 1-28
- Publication date:
- 2026-02-18
- Acceptance date:
- 2026-01-21
- DOI:
- EISSN:
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1464-3839
- ISSN:
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0013-0915
- Language:
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English
- Keywords:
- Source identifiers:
-
3770181
- Deposit date:
-
2026-02-18
- ARK identifier:
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- Copyright date:
- 2026
- Licence:
- CC Attribution (CC BY)
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