Artin L-functions of small conductor

John W. Jones, David P. Roberts

    Research output: Contribution to journalArticlepeer-review

    2 Scopus citations


    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 languageEnglish (US)
    Article number16
    JournalResearch in Number Theory
    Issue number1
    StatePublished - 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.

    Publisher Copyright:
    © 2017, The Author(s).


    • Artin representation
    • Conductor
    • L-function
    • Number field


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