On the sum of two primitive elements of maximal subfields of a finite field.
type: Item
instance of: scholarly article
title: On the sum of two primitive elements of maximal subfields of a finite field.
zbMATH Open document ID: 1081.11079
DOI: 10.1016/S1071-5797(02)00014-X
published in: Finite Fields and their Applications
publication date: 2003-04-02T00:00:00Z
review text: Let \(K\) be a finite field and \(L=K(a),L'=K(a')\) be extensions of degree \(d,d'\). The author is motivated by 'when is \(K(a,a')=K(a+a')\) for \(\gcd(d,d')>1\)?' Let \(q\) be a power of a prime and \(p,p',p''\) distinct primes. Put \(y=pp',y'=pp'',z=\text{lcm}(y,y')\) and \(K=F_{q^y},K'=F_{q^{y'}},L=F_{q^z}\). Define \[ A=\{(a,a')\in K\times K'mid F_q(a)=K,F_q(a')=K',F_q(a+a')\neq L\}. \] The author expresses the cardinality of \(A\) in terms of \(q,p,p',p''\) and gives several applications to counting points in algebraic sets.
Mathematics Subject Classification ID: 11T30
Mathematics Subject Classification ID: 12E20
zbMATH DE Number: 1891476
zbMATH Keywords: Abelian field extension
zbMATH Keywords: algebraic set
zbMATH Keywords: field compositum
zbMATH Keywords: finite field
author: Bogdan V. Petrenko
reviewed by: G. H. Norton
describes a project that uses: Magma
MaRDI profile type: Publication
cites work: Addition of sequences in general fields
cites work: Q3997571
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cites work: Degrees of Sums in a Separable Field Extension
cites work: Q4784966
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cites work: Numbers of solutions of equations in finite fields
full work available at URL: s1071-5797(02)00014-x
OpenAlex ID: W2058627629
description: scientific article; zbMATH DE number 1891476