2018/03/31 by Andrew R. Booker, Min Lee, Andreas Strömbergsson
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Conductor #Conjecture #Limit (mathematics) #Representation (politics) #Selberg trace formula #TRACE (psycholinguistics) #math.NT
paper · pdf · doi:10.1112/jlms.12349
64 pages, to appear in JLMS
openalex created_date 2018/03/29 · arxiv created 2020/04/17 · openalex publication_date 2020/06/23 · arxiv updated 2020/07/01 · openalex updated_date 2026/08/05
We derive a fully explicit version of the Selberg trace formula for twist-minimal Maass forms of weight 0 and arbitrary conductor and nebentypus character, and apply it to prove two theorems. First, conditional on Artin's conjecture, we classify the even 2-dimensional Artin representations of small conductor; in particular, we show that the even icosahedral representation of smallest conductor is the one found by Doud and Moore (J. Number