The fourth moment of quadratic Dirichlet L-functions over function fields

We obtain an asymptotic formula for the fourth moment of quadratic Dirichlet L-functions over , as the base field is fixed and the genus of the family goes to infinity. According to conjectures of Andrade and Keating, we expect the fourth moment to be asymptotic to up to an error of size , where P is a polynomial of degree 10 with explicit coefficients. We prove an asymptotic formula with the leading three terms, which agrees with the conjectured result.