A POLYNOMIAL ROTH THEOREM FOR CORNERS IN FINITE FIELDS
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 A ⊂ F p × F p with | A | > p 2 − 1 16 contains three points ( x 1 , x 2 ) , ( x 1 + ϕ 1 ( y ) , x 2 ) , ( x 1 , x 2 + ϕ 2 ( y ) ) . The study of these questions on F p was started by Bourgain and Chang. Our Theorem adapts the argument of Dong, Li, and Sawin, in...
Paper Details
Title
A POLYNOMIAL ROTH THEOREM FOR CORNERS IN FINITE FIELDS
Published Date
Aug 16, 2021
Journal
Volume
67
Issue
4
Pages
885 - 896
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