Abstract
We obtain polylogarithmic bounds in the polynomial Szemerédi theorem when the polynomials have distinct degrees and zero constant terms. Specifically, let <ani:inline-formula id="ieq1"><ani:alternatives><ani:tex-math>$A$</ani:tex-math></ani:alternatives> </ani:inline-formula>.
| Original language | English |
|---|---|
| Journal | Proceedings of the Royal Society of Edinburgh Section A: Mathematics |
| DOIs | |
| State | Accepted/In press - 2025 |
Bibliographical note
Publisher Copyright:© The Author(s), 2025. Published by Cambridge University Press.
Funding
The authors thank Sean Prendiville for valuable discussions, particularly regarding an earlier version of the proof of , and for his encouragement. We are grateful to the anonymous referee for a careful reading of the paper and for numerous helpful comments and corrections. XS was supported by NSF grant DMS-2200565. MW was partially supported by the Swiss National Science Foundation grant TMSGI2-2112.
| Funders | Funder number |
|---|---|
| National Science Foundation Arctic Social Science Program | DMS-2200565 |
| Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung | TMSGI2-2112 |
Keywords
- polynomial Szemerédi theorem
- popular differences
ASJC Scopus subject areas
- General Mathematics
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