A Riemann Hypothesis for characteristic p L-functions

1999/07/31 by David Goss
Mathematics · #math.NT #msc:11G09

paper · pdf

published as Journal of Number Theory, vol. 82 (June 2000), 299-322 · This is the final version (with new title) as it will appear in the Journal of Number Theory

arxiv created 1999/12/01 · arxiv updated 2009/11/30

Abstract

We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute values. Further we use absolute values to give similar reformulations of the classical conjectures (with, perhaps, finitely many exceptional zeroes). We show how both sets of conjectures behave in remarkably similar ways.

Related

• The impact of the infinite primes on the Riemann hypothesis for characteristic p L-series
• Investigation about a statement equivalent to Riemann Hypothesis (RH) applied to Dirichlet primitive L functions
• The Generalized Riemann Hypothesis from zeros of a single L-function
• Hardy-Littlewood-Riesz type equivalent criteria for the Generalized Riemann hypothesis
• Equivalent criteria for the Riemann hypothesis for a general class of L-functions