On the coefficients of the Zeta-function's L-polynomial for algebraic function fields over finite constant fields

Abstract

We give an explicit formula of the coefficients of the Zeta-Function's L-polynomial for algebraic function fields over finite constant fields. Thus, we deduce an expression of the class number of algebraic function fields defined over finite fields. Moreover, we give an application of this formula in the case of the curves of defect 2 defined over $\mathbb{F}_2$.