Twist-minimal trace formulas and the Selberg eigenvalue conjecture

Andrew R Booker, Min Lee, Andreas Strömbergsson

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

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 [DM06], of conductor 1951. Second, we verify the Selberg eigenvalue conjecture for groups of small level, improving on a result of Huxley [Hux85] from 1985.
Original languageEnglish
JournalJournal of the London Mathematical Society
Early online date23 Jun 2020
DOIs
Publication statusE-pub ahead of print - 23 Jun 2020

Keywords

  • 11F12
  • 11F72 (primary)
  • 11F80 (secondary)

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