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.
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 language | English |
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Journal | Journal of the London Mathematical Society |
Early online date | 23 Jun 2020 |
DOIs | |
Publication status | E-pub ahead of print - 23 Jun 2020 |
Keywords
- 11F12
- 11F72 (primary)
- 11F80 (secondary)