The a-numbers of Fermat and Hurwitz curves

For an algebraic curve X defined over an algebraically closed field of characteristic p>0, the a-number a(X) is the dimension of the space of exact holomorphic differentials on X. We compute the a-number for infinite families of Fermat and Hurwitz curves. As our results apply to Hermitian curves, we recover a previous result by Gross [10].