5 papers · 1 filter
averages of the Fourier transform in finite fields
Jonathan M. Fraser
The Fourier transform plays a central role in many geometric and combinatorial problems cast in vector spaces over finite fields. If a set admits optimal bounds on its F…
averages of the discrete Fourier transform and applications
Jonathan M. Fraser, Firdavs Rakhmonov
The discrete Fourier transform has proven to be an essential tool in many geometric and combinatorial problems in vector spaces over finite fields. In general, sets with good unifo…
Fourier analytic properties of Kakeya sets in finite fields
Jonathan M. Fraser
We prove that a Kakeya set in a vector space over a finite field of size always supports a probability measure whose Fourier transform is bounded by for all non-zero f…
An improved restriction theorem in finite fields
Jonathan M. Fraser, Firdavs Rakhmonov
Mockenhaupt and Tao (Duke 2004) proved a finite field analogue of the Stein--Tomas restriction theorem, establishing a range of for which restriction estimates hol…
Exceptional projections in finite fields: Fourier analytic bounds and incidence geometry
Jonathan M. Fraser, Firdavs Rakhmonov
We consider the problem of bounding the number of exceptional projections (projections which are smaller than typical) of a subset of a vector space over a finite field onto subspa…