Artin Conjecture for p-adic Galois Representations of Function Fields

Research paper by Ruochuan Liu, Daqing Wan

Indexed on: 03 Jan '16Published on: 03 Jan '16Published in: Mathematics - Number Theory


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.