The integrated fourth moment of Dirichlet L-functions over rational function fields

Abstract

We consider the hybrid fourth shifted moment of Dirichlet L-functions over rational function fields, where the moment average is taken over all odd primitive characters of modulus Q∈Fq[t] and over the critical circle, which is the symmetry line of the corresponding functional equation. We obtain an asymptotic formula for this moment with the full main term for arbitrary modulus Q, as deg⁡Q→∞ and q is fixed. Moreover, in case of an irreducible modulus Q we get an exact formula for this hybrid moment.