On the sum of two primitive elements of maximal subfields of a finite field.
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.
scientific article; zbMATH DE number 1891476