Li's criterion and the Riemann hypothesis for function fields II

Abstract

In a previous paper [4], we extended the Li criterion for the Riemann hypothesis for a function field K of genus g over a finite field Fq. More recently, further numerical computations of the Li coefficients for the Dirichlet and Hecke L-functions have led to the conjecture that they are positive and increasing under the Riemann hypothesis. In this paper, we show the that the Li coefficients λK(n) for the function field K are increasing in n.