Estimates for coefficients of \(L\)-functions for function fields (Q1284213)

Let \(A= \mathbb{F}_q [T]\) and let \(\chi: (A/\Delta A)^*\to \mathbb{C}^*\) be a ``Dirichlet character''. Associated to \(\chi\) one has the classical complex \(L\)-series \(L(\chi,u)\); by the classical results of A. Weil, \(L(\chi,u)\) is a polynomial in \(u\). The author studies the coefficients of this polynomial using the ideas of Burgess and then applies to fundamental units in ``real'' quadratic function fields.