Normal and primitive normal elements with prescribed traces in intermediate extensions of finite fields

2025/10/16 by Mazumder, Arpan Chandra, Kapetanakis, Giorgos, Basnet, Dhiren Kumar
#11T24 #12E20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2510.14840

Abstract

In this article, we study the existence and distribution of elements in finite field extensions with prescribed traces in several intermediate extensions that are also either normal or primitive normal. In the former case, we fully characterize the conditions under which such elements exist and provide an explicit enumeration of these elements. In the latter case we provide asymptotic results.

Citations

• The modified prime sieve for primitive elements in finite fields
• Hybrid bounds for prime divisors
• Four consecutive primitive elements in a finite field
• The Strong Primitive Normal Basis Theorem

Cited by

• Translates of completely normal elements and the Morgan-Mullen conjecture

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