The moments and statistical distribution of class number of primes over function fields

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