Artin conjecture for p-adic Galois representations of function fields

摘要

For a global function field K of positive characteristic p, we show that Artin's entireness 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.