On additive polynomials and certain maximal curves

We show that a maximal curve over Fq2Fq2 given by an equation A(X)=F(Y)A(X)=F(Y), where A(X)∈Fq2[X]A(X)∈Fq2[X] is additive and separable and where F(Y)∈Fq2[Y]F(Y)∈Fq2[Y] has degree mm prime to the characteristic pp, is such that all roots of A(X)A(X) belong to Fq2Fq2. In the particular case where F(Y)=YmF(Y)=Ym, we show that the degree mm is a divisor of q+1q+1.