Author(s) :
Florin Nicolae
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 09-2013
MSC 2000
- 11R42 Zeta functions and $L$-functions of number fields
Abstract :
Let $K/\Q$ be a finite Galois extension, $s_0\in \C\setminus \{1\}$,
$Hol(s_0)$ the semigroup of Artin L-functions holomorphic at $s_0$.
We present criteria for Artin's holomorphy conjecture in terms of the
semigroup $Hol(s_0)$. We conjecture that Artin's L-functions are holomorphic
at $s_0$ if and only if $Hol(s_0)$ is factorial. We prove this if $s_0$ is a
zero of an L-function associated to a linear character of the Galois
group.
Keywords :
Artin L-function; Artin's holomorphy conjecture