Let 𝔽 qd be the d-dimensional vector space over the finite field 𝔽 q with q elements. For
each non-zero r in 𝔽 q and E⊂ 𝔽 qd, we define W⁢(r) as the number of quadruples (x, y, z …

We investigate the size of the distance set determined by two subsets of finite dimensional
vector spaces over finite fields. A lower bound of the size is given explicitly in terms of …

Let 𝔽 q be a finite field of q elements, where q is a large odd prime power and Q= a 1⁢ x 1 c
1+⋯+ ad⁢ xdcd∈ 𝔽 q⁢[x 1,…, xd], where 2≤ ci≤ N, gcd⁡(ci, q)= 1, and ai∈ 𝔽 q for all 1≤ …

On the additive energy of the distance set in finite fields - ScienceDirect Skip to main contentSkip
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Additive Combinatorics over Finite Fields: New Results and Applications. Page 245 Igor E.
Shparlinski Additive Combinatorics over Finite Fields: New Results and Applications Abstract …

The famous Erdős-Falconer distance problems aim to quantify the extent to which large sets
must determine many distinct distances. The problems in both the Euclidean setting and the …

We prove that if we are given a set of points 𝒫 and set of lines ℒ in 𝔽 q 2 such that| 𝒫|⁢| ℒ|≳
q 8/3, then the set of distinct distances between points from 𝒫 and lines from ℒ contains a …

Given, with the finite field of order q and the integer, we define the two-parameter distance
set. Birklbauer and Iosevich ['A two-parameter finite field Erdős–Falconer distance problem' …

In this paper, we study the distance problem in the setting of finite p-adic rings. In odd
dimensions, our results are essentially sharp. In even dimensions, we clarify the conjecture …

In this paper we study the generalized Erdős–Falconer distance problems in the finite field
setting via spectra of directed graph. The generalized distances are defined in terms of …