Moments of Artin-Schreier L-functions

We compute moments of L-functions associated to the polynomial family of Artin-Schreier covers over F-q , where q is a power of a prime p > 2, when the size of the finite field is fixed and the genus of the family goes to infinity. More specifically, we compute the k th moment for a large range of values of k , depending on the sizes ofp p and q . We also compute the second moment in absolute value of the polynomial family, obtaining an exact formula with a lower order term, and confirming the unitary symmetry type of the family.