Mathematical Research Letters
Volume 25 (2018)
Artin conjecture for $p$-adic Galois representations of function fields
Pages: 143 – 157
For a global function field $K$ of positive characteristic $p$, we show that Artin’s entireness conjecture for L-functions of geometric padic 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.
Received 11 January 2016