The number of occurrences of a fixed spread among n directions in vector spaces over finite fields

TL;DR

This paper investigates the maximum frequency of a specific angle appearing among n directions in vector spaces over finite fields, providing a finite field analog to a classical geometric problem.

Contribution

It introduces a finite field analog of a geometric problem concerning angles among directions, extending classical results to finite vector spaces.

Findings

Derived bounds for the maximum number of fixed angle occurrences

Extended classical geometric problems to finite field contexts

Provided new insights into combinatorial geometry over finite fields

Abstract

We study a finite analog of a problem of Erdos, Hickerson and Pach on the maximum number of occurrences of a fixed angle among n directions in three-dimensional spaces.