Estimates for Coefficients of L-Functions for Function Fields

Author: Cohen C-N.S.D.

Source: Finite Fields and Their Applications, Volume 5, Number 1, January 1999 , pp. 76-88(13)

Publisher: Academic Press

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Abstract:

We consider the Dirichlet characters for polynomial rings Fopf _q[T] and the associated L-functions. By Weil's result, the associated L-functions are all polynomials. Applying Burgess' idea, we obtain an upper bound for the coefficients of these L-functions. As an application, using our estimates, we obtain an upper bound for the degree of the fundamental unit in real quadratic function fields. Copyright 1999 Academic Press.