We investigate the moment and the distribution of L(1, χP ),
where χP varies over quadratic characters associated to irreducible polynomials P of degree 2g + 1 over Fq[T] as g → ∞. In the first part of
the paper, we compute the integral moments of the class number hP
associated to quadratic function fields with prime discriminants ...
We investigate the moment and the distribution of L(1, χP ),
where χP varies over quadratic characters associated to irreducible polynomials P of degree 2g + 1 over Fq[T] as g → ∞. In the first part of
the paper, we compute the integral moments of the class number hP
associated to quadratic function fields with prime discriminants P, and
this is done by adapting to the function field setting some of the previous results carried out by Nagoshi in the number field setting. In the
second part of the paper, we compute the complex moments of L(1, χP )
in large uniform range and investigate the statistical distribution of the
class numbers by introducing a certain random Euler product. The second part of the paper is based on recent results carried out by Lumley
when dealing with square-free polynomials.