%0 Journal Article
%T Pairs of dot products in finite fields and rings
%A David Covert
%A Steven Senger
%J Mathematics
%D 2015
%I arXiv
%X We obtain bounds on the number of triples that determine a given pair of dot products arising in a vector space over a finite field or a module over the set of integers modulo a power of a prime. More precisely, given $E\subset \mathbb F_q^d$ or $\mathbb Z_q^d$, we provide bounds on the size of the set \[\left\{(u,v,w)\in E \times E \times E : u\cdot v = \alpha, u \cdot w = \beta \right\}\] for units $\alpha$ and $\beta$.
%U http://arxiv.org/abs/1508.02691v1