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

Journal Title

Springer Proceedings in Mathematics and Statistics

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