Pairs of Dot Products in Finite Fields and Rings
Abstract
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 (Formula presented) or (Formula presented), we provide bounds on the size of the set {(u, v, w) ∈ E × E × E: u ⋅ v = α, u ⋅ w = β} for units α and β.
Department(s)
Mathematics
Document Type
Conference Proceeding
DOI
https://doi.org/10.1007/978-3-319-68032-3_8
Keywords
Dot-product sets, Finite fields, Sum-product problem
Publication Date
1-1-2017
Recommended Citation
Covert, David, and Steven Senger. "Pairs of dot products in finite fields and rings." In Combinatorial and Additive Number Theory II, pp. 129-138. Springer, Cham, 2015.
Journal Title
Springer Proceedings in Mathematics and Statistics
COinS
