Artin Conjecture for p-adic Galois Representations of Function Fields
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Artin Conjecture for p-adic Galois Representations of Function Fields

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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