Artin Conjecture for p-adic Galois Representations of Function Fields

2016/01/03 by Liu, Ruochuan, Wan, Daqing
#11G40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1601.00267

Abstract

For a global function field K of positive characteristic p, we show that Artin conjecture for L-functions of geometric p-adic Galois representations of K is true in a non-trivial p-adic disk but is false in the full p-adic plane. In particular, we prove the non-rationality of the geometric unit root L-functions.

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