David Covert

On the Sums of Any

For a set

k

E\subset \mathbb F_q^d

Points in Finite Fields

, we define the

The k-resultant modulus set problem on algebraic varieties over finite fields

k

Pairs of dot products in finite fields and rings

-resultant magnitude set as

The Generalized k-Resultant Modulus Set Problem in Finite Fields

\Delta_k(E) =\{\|\textbf{x}_1 + \dots + \textbf{x}_k\|\in \mathbb F_q: \textbf{x}_1, \dots, \textbf{x}_k \in E\},

LONG PATHS IN THE DISTANCE GRAPH OVER LARGE SUBSETS OF VECTOR SPACES OVER FINITE FIELDS

where

Generalized incidence theorems, homogeneous forms and sum-product estimates in finite fields

\|\textbf{v}\|=v_1^2+\cdots+ v_d^2

Geometric configurations in the ring of integers modulo p^{ell}

for

A Furstenberg-Katznelson-Weiss type theorem on (d+1) -point configurations in sets of positive density in finite field geometries

\textbf{v}=(v_1, \ldots, v_d) \in \mathbb F_q^d.