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.
Bibliographical noteFunding 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.
- Artin representation
- Number field