Document Type
Article
Publication Date
10-1-2021
Abstract
We prove a Roth-type theorem for polynomial corners in the finite field setting. Let ϕ1 and ϕ2 be two polynomials of distinct degree. For sufficiently large primes p, any subset (Formula presented.) with (Formula presented.) contains three points (Formula presented.). The study of these questions on (Formula presented.) was started by Bourgain and Chang. Our Theorem adapts the argument of Dong, Li, and Sawin, in particular relying upon deep Weil-type inequalities established by N. Katz.
Publication Source (Journal or Book title)
Mathematika
First Page
885
Last Page
896
Recommended Citation
Han, R., Lacey, M., & Yang, F. (2021). A POLYNOMIAL ROTH THEOREM FOR CORNERS IN FINITE FIELDS. Mathematika, 67 (4), 885-896. https://doi.org/10.1112/mtk.12108
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