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On holomorphic Artin L-functions

Name: On holomorphic Artin L-functions
Creator: Florin Nicolae
Keywords: Mathematics - Number Theory, FOS: Mathematics, 510 Mathematik, Number Theory (math.NT), ddc:510, Artin L-function, Artin's holomorphy conjecture, 11R42

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type , Preprint , Research 20 Oct 2017Embargo end date: 17 Dec 2021 Germany Publisher:Springer Science and Business Media LLCJournal:Monatshefte für Mathematik, volume 186, pages 679-683 (issn: 0026-9255, eissn: 1436-5081,

Authors: Florin Nicolae;

doi: 10.1007/s00605-017-1120-4 , 10.14279/depositonce-14560 , 10.48550/arxiv.1610.08651

arXiv: http://arxiv.org/abs/1610.08651

On holomorphic Artin L-functions

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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.

Country

Germany

Related Organizations

Technical University of Berlin
Germany
Romanian Academy
Romania

Keywords

Mathematics - Number Theory, FOS: Mathematics, 510 Mathematik, Number Theory (math.NT), Artin L-function, Artin's holomorphy conjecture, 11R42, ddc: ddc:510

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