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.
© 2017, The Author(s).
- Artin representation
- Number field