We prove that a sufficiently large subset of the d-dimensional vector space over a finite field with q elements, Fq , contains a copy of every k-simplex. Fourier analytic methods, Kloosterman sums,… (More)

We prove that if A ⊂ Fq is such that |A| > q 12+ 1 2d , then F ∗ q ⊂ dA = A + · · ·+A d times, where A = {a · a′ : a, a′ ∈ A}, and where F∗q denotes the multiplicative group of the finite field Fq.… (More)

Before we state our main theorems, we begin with some notation: given a finite subset A of some commutative ring, we let A + A denote the set of sums a + b, where a, b ∈ A; and, we let A.A denote the… (More)

We prove that if the cardinality of a subset of the 2-dimensional vector space over a finite field with q elements is ≥ ρq, with 1 √ q << ρ ≤ 1, then it contains an isometric copy of ≥ cρq triangles.

In this paper we systematically study various properties of the distance graph in Fq , the d-dimensional vector space over the finite field Fq with q elements. In the process we compute the diameter… (More)

We study the distribution of palindromic numbers (with respect to a fixed base g ≥ 2) over certain congruence classes, and we derive a nontrivial upper bound for the number of prime palindromes n ≤ x… (More)

This article is based on the series of lectures on the interaction of Fourier analysis and geometric combinatorics delivered by the author in Padova at the Minicorsi di Analisi Matematica in June,… (More)

We will prove a theorem below (Theorem 1), which holds for the polynomial ring C[x] unconditionally; but, under the assumption of a certain 24-term version of Fermat’s Last Theorem, it holds for Z+,… (More)

An analog of the Falconer distance problem in vector spaces over finite fields asks for the threshold α > 0 such that |∆(E)| & q whenever |E| & q, where E ⊂ Fq , the d-dimensional vector space over a… (More)