Averaging Quadratic L-Functions over Function Fields

The problem of averaging quadratic L-functions dates back to Gauss, who (essentially) conjectured an average value for the class numbers of quadratic fields, which of course is connected to the the average of certain quadratic L-functions at s=1. We will discuss a formula for the average value of L-functions associated to a set of quadratic function fields ramified at one finite place and infinity, which are analogous to the imaginary quadratic fields Q(sqrt(-p)) for a prime number p.