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Main Title: On holomorphic Artin L-functions
Author(s): Nicolae, Florin
Type: Research Paper
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.
Subject(s): Artin L-function
Artin's holomorphy conjecture
Issue Date: 25-Mar-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 11R42 Zeta functions and L-functions of number fields
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 09
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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