Estimates for coefficients of \(L\)-functions for function fields
type: Item
instance of: scholarly article
title: Estimates for coefficients of \(L\)-functions for function fields
zbMATH Open document ID: 0948.11044
author: Chih-Nung Hsu
published in: Finite Fields and their Applications
publication date: 1999-06-14T00:00:00Z
review text: 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.
reviewed by: David Goss
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 11M26
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 11T55
Mathematics Subject Classification ID: 11R27
zbMATH DE Number: 1271778
zbMATH Keywords: Weil \(L\)-series
zbMATH Keywords: Riemann hypothesis
zbMATH Keywords: Burgers estimate
zbMATH Keywords: fundamental unit
MaRDI profile type: Publication
full work available at URL: ffta.1998.0234
OpenAlex ID: W2090688116
cites work: On Character Sums and Primitive Roots†
cites work: On Character Sums and L-Series†
cites work: Q4001344
cites work: Explicit Class Field Theory for Rational Function Fields
cites work: Q3815392
cites work: Q3998729
DOI: 10.1006/FFTA.1998.0234
description: scientific article; zbMATH DE number 1271778