October 9, 2025
1:50 pm
-
2:45 pm
Math Tower (MW) 154
Shukun Wu
Indiana University Bloomington
Title
Bilinear estimates in F_p with application in Roth-type result
Abstract
We improve an L^2 × L^2 -> L^2 estimate for a certain bilinear operator in the finite field of size p, where p is a prime sufficiently large. Our method carefully picks the variables to apply the Cauchy-Schwarz inequality. As a corollary, we show that there exists a quadratic progression x,x+y,x+y2 for nonzero y inside any subset of F_p of density >= p^{−1/8}. This is joint work with Necef Kavrut.