Character sums over affine spaces and applications

2020/07/09 by Lucas Reis, Reis, Lucas · 1 citation
Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2007.04859

openalex publication_date 2020/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finite field \mathbb F_q, a positive integer n and an \mathbb F_q-affine space \mathcal A⊆ \mathbb F_qⁿ, we provide a new bound on the sum ∑_{a∈ \mathcal A}χ(a), where χ a multiplicative character of \mathbb F_qⁿ. We focus on the applicability of our estimate to results regarding the existence of special primitive elements in \mathbb F_qⁿ. In particular, we obtain substantial improvements on previous works.

Cited by

• Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields, II

Related

• Multiplicative character sums over two classes of subsets of quadratic extensions of finite fields
• Character sums over elements of extensions of finite fields with restricted coordinates
• Character sums over sparse elements of finite fields
• On a generalization of Jacobi sums
• On character sums over flat numbers