A note on additive characters of finite fields

2020/05/02 by Reis, Lucas · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.00911

Abstract

Let \mathbb F_q be the finite field with q elements, where q is a prime power and, for each integer n≥ 1, let \mathbb F_qⁿ be the unique n-degree extension of \mathbb F_q. The \mathbb F_q-orders of an element in \mathbb F_qⁿ and an additive character over \mathbb F_qⁿ have been extensively used in the proof of existence results over finite fields (e.g., the Primitive Normal Basis Theorem). In this note we provide an interesting relation between these two objects.

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