Mean value of the class number in function fields revisited

In this paper an asymptotic formula for the sum ∑ L ( 1 , χ ) is established for the family of quadratic Dirichlet L -functions over the rational function field over a finite field F q with q fixed. Using the recent techniques developed by Florea we obtain an extra lower order terms that was never been predicted in number fields and function fields. As a corollary, we obtain a formula for the average of the class number over function fields which also contains strenuous lower order terms and so improving on previous results of Hoffstein and Rosen.