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arXiv · 1601.00267

Artin Conjecture for p-adic Galois Representations of Function Fields

Ruochuan Liu·Daqing Wan
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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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Ruochuan Liu, Daqing Wan. 2017-02-23. Artin Conjecture for p-adic Galois Representations of Function Fields. https://arxiv.org/abs/1601.00267

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