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

Alvarez Arturo

Published 2013-05-17, updated 2014-09-19Version 4

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.