Appendix: Ray class characters of bounded order and bounded conductor

Appendix to: A. Karnataki, Self-dual Artin representations of dimension three. Journal of Number Theory, v. 173, pp. 442 - 446. https://doi.org/10.1016/j.jnt.2016.09.00

Quaternionic Artin representations of Q

Isomorphism classes of dihedral Artin representations of ℚ can be counted asymptotically using Siegel's asymptotic averages of class numbers of binary quadratic forms. Here we consider the analogous problem for quaternionic representations. While an asymptotic formula is out of our reach in this case, we show that the asymptotic behaviour in the two cases is quite different