A calculation of $L$-series in terms of Jacobi sums

Abstract

Let us consider a cyclic extension of a function field defined over a finite field. For a character (non-trivial) of this extension, we calculate, as a linear combinations of products of Jacobi sums, the coefficients of the polynomial given by its Dirichtlet $L$-series. In the last section we show applications of this calculation.

arXiv comment18 Pages, Added a new section

References in corpus (1)

• The $p$-rank of the reduction $\mathrm{mod}\mathrm{p}$ of jacobians and Jacobi sums