Artin L-functions of small conductor

John W. Jones; David P. Roberts

doi:10.1007/s40993-017-0079-5

Artin L-functions of small conductor

John W. Jones, David P. Roberts

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study the problem of finding the Artin L-functions with the smallest conductor for a given Galois type. We adapt standard analytic techniques to our novel situation of fixed Galois type and obtain much improved lower bounds on the smallest conductor. For small Galois types we use complete tables of number fields to determine the actual smallest conductor.

Original language	English (US)
Article number	16
Journal	Research in Number Theory
Volume	3
Issue number	1
DOIs	https://doi.org/10.1007/s40993-017-0079-5
State	Published - Dec 1 2017

Bibliographical note

Funding Information:
DPR?s work on this paper was supported by Grant #209472 from the Simons Foundation and Grant DMS-1601350 from the National Science Foundation. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Keywords

Artin representation
Conductor
L-function
Number field

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