Self-dual Artin representations of dimension three (with an appendix by David E. Rohrlich)

Abstract

We give an unconditional proof that self-dual Artin representations of $\mathbb{Q}$ of dimension $3$ have density $0$ among all Artin representations of $\mathbb{Q}$ of dimension $3$. Previously this was known under the assumption of Malle's Conjecture.

Appendix by David E. Rohrlich