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October 3, 2025Open Access

Incidence theorems for multivariate polynomials over finite fields

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Authors

CSChong ShangguanYYYu-Sheng YangTZTao Zhang

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Overview

Proving incidence bounds for multivariate polynomials reveals connections to Cayley color graphs, indicating new properties of incidences.

Key Points

  • Strengthened bounds on the number of incidences between multivariate polynomials and points have been established.
  • The results offer asymptotically tight bounds under a wide range of parameters, enhancing previous findings.
  • A novel connection between the incidence problem and Cayley color graphs is introduced, aiding the analysis.
  • An expander mixing lemma is proven for abelian Cayley color graphs, extending classical mixing lemmas.

Cite This Study

Shangguan et al. (2025) studied this question.

synapsesocial.com/papers/68e0450fa99c246f578b3f2bhttps://doi.org/10.48550/arxiv.2509.17563
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