Averages of the Fourier transform in finite fields

Abstract: Discrete Fourier analysis is a useful tool in various counting problems in vector spaces over finite fields. I will mention some results in this direction, with emphasis on a new approach based on quantifying Fourier decay via a spectrum of exponents coming from certain $L^p$ averages.

Mathematics

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2025)