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Solving polynomials in large pseudo-finite sets

  • Alessandro Vegnuti
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Abstract

Using techniques from model theory, we prove analogues of Rado's and Sárközy's theorems on solutions to polynomial equations in dense sets of definable groups and fields equipped with well-behaved measures. As a special case, we adapt our results to pseudofinite structures, to deduce non-qualitative asymptotic results.

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Cite

BibTeXRIS
BibTeX
@misc{vegnuti2026solving,
  title = {{Solving polynomials in large pseudo-finite sets}},
  author = {Alessandro Vegnuti},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08211},
  eprint = {2611.08211},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08211},
}
RIS
TY  - UNPB
TI  - Solving polynomials in large pseudo-finite sets
AU  - Alessandro Vegnuti
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08211
UR  - https://arxiv.org/abs/2611.08211
AB  - Using techniques from model theory, we prove analogues of Rado's and Sárközy's theorems on solutions to polynomial equations in dense sets of definable groups and fields equipped with well-behaved measures. As a special case, we adapt our results to pseudofinite structures, to deduce non-qualitative asymptotic results.
ER  -