Character sums over affine spaces and applications

Given a finite field Fq, a positive integer n and an Fq-affine space A⊆Fqn, we show that a result of Katz provides a new bound on the sum ∑a∈Aχ(a), where χ is a multiplicative character of Fqn. The paper is focused on the applicability of this estimate to results regarding the existence of special p...

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Bibliographic Details
Published in:Finite fields and their applications 2022-10, Vol.83, p.102067, Article 102067
Main Author: Reis, Lucas
Format: Article
Language:English
Subjects:
Affine spaces
Character sums
Finite fields
Primitive elements
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Summary:Given a finite field Fq, a positive integer n and an Fq-affine space A⊆Fqn, we show that a result of Katz provides a new bound on the sum ∑a∈Aχ(a), where χ is a multiplicative character of Fqn. The paper is focused on the applicability of this estimate to results regarding the existence of special primitive elements in Fqn. In particular, we obtain substantial improvements on previous works.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2022.102067