Extremal behaviour of ±1-valued completely multiplicative functions in function fields

Abstract

We investigate the classical Polya and Turan conjectures in the context of rational function fields over finite fields Fq. Related to these two conjectures we investigate the sign of truncations of Dirichlet L-functions at point s = 1 corresponding to quadratic characters over Fq[t], prove a variant of a theorem of Landau for arbitrary sets of monic, irreducible polynomials over Fq[t] and calculate the mean value of certain variants of the Liouville function over Fq[t].