Let G be a finite abelian group. Let f: G→ C be a signal (ie function). The classical
uncertainty principle asserts that the product of the size of the support of f and its Fourier …

The Fourier restriction phenomenon and the size of Kakeya sets are explored in the setting
of the ring of integers modulo $ N $ for general $ N $ and a striking similarity with the …

The first purpose of this paper is to provide new finite field extension theorems for
paraboloids and spheres. By using the unusual good Fourier transform of the zero sphere in …

We apply geometric incidence estimates in positive characteristic to prove the optimal L 2→
L 3 Fourier extension estimate for the paraboloid in the four-dimensional vector space over a …

In 2005 Bourgain gave the first explicit construction of a two‐source extractor family with min‐
entropy rate less than 1/2. His approach combined Fourier analysis with innovative but …

On Restriction Estimates for the Zero Radius Sphere over Finite Fields Page 1 Canad. J. Math.
Vol. ( ), pp. – http://dx.doi.org/ . /SX © Canadian Mathematical Society On Restriction Estimates …

Let $ G $ be a finite abelian group. Let $ f: G\to {\mathbb C} $ be a signal (ie function). The
classical uncertainty principle asserts that the product of the size of the support of $ f $ and …

In this paper, we provide a general framework for counting geometric structures in pseudo-
random graphs. As applications, our theorems recover and improve several results on the …

We study a variant of the Erdős–Falconer distance problem in the setting of finite fields. More
precisely, let E and F be sets in F _q^ d F qd, and Δ (E), Δ (F) Δ (E), Δ (F) be corresponding …

Given $ A\subset F_ {p}^ 2$ a sufficiently small set in the plane over a prime residue field,
we prove that there are at most $ O_\epsilon (| A|^{\frac {99}{41}+\epsilon}) $ rectangles with …