Please use this identifier to cite or link to this item:
https://doi.org/10.19086/da.55555
DC Field | Value | |
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dc.title | Semialgebraic Methods and Generalized Sum-Product Phenomena | |
dc.contributor.author | Jing, Y | |
dc.contributor.author | Roy, S | |
dc.contributor.author | Tran, CM | |
dc.date.accessioned | 2023-07-10T02:47:11Z | |
dc.date.available | 2023-07-10T02:47:11Z | |
dc.date.issued | 2022-01-01 | |
dc.identifier.citation | Jing, Y, Roy, S, Tran, CM (2022-01-01). Semialgebraic Methods and Generalized Sum-Product Phenomena. Discrete Analysis 2022. ScholarBank@NUS Repository. https://doi.org/10.19086/da.55555 | |
dc.identifier.issn | 2397-3129 | |
dc.identifier.uri | https://scholarbank.nus.edu.sg/handle/10635/242963 | |
dc.description.abstract | For a bivariate [Formula Presented] our first result shows that for all finite A ⊆ R, |P(A,A)| ≥ α|A|5/4 with α = α(degP) ∈ R>0 unless P(x,y) = f (γu(x)+δu(y)) or P(x,y) = f (um(x)un(y)) for some univariate f,u ∈ R[t] \R, constants γ,δ ∈R≠0, and m,n ∈N≥1. This resolves the symmetric nonexpanders classification problem proposed by de Zeeuw. Our second and third results are sum-product type theorems for two polynomials, generalizing the classical result by Erdős and Szemerédi as well as a theorem by Shen. We also obtain similar results for C, and from this deduce results for fields of characteristic 0 and fields of large prime characteristic. The proofs of our results use tools from semialgebraic/o-minimal geometry | |
dc.source | Elements | |
dc.type | Article | |
dc.date.updated | 2023-07-07T15:53:17Z | |
dc.contributor.department | MATHEMATICS | |
dc.description.doi | 10.19086/da.55555 | |
dc.description.sourcetitle | Discrete Analysis | |
dc.description.volume | 2022 | |
dc.published.state | Published | |
Appears in Collections: | Elements Staff Publications |
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https:arxiv.org:pdf:1910.04904.pdf | 452.36 kB | Adobe PDF | OPEN | Published | View/Download |
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