Quaternionic Artin representations and nontraditional arithmetic statistics

Abstract

We classify and then attempt to count the real quadratic fields (ordered by the size of the totally positive fundamental unit, as in Sarnak [14], [15]) from which quaternionic Artin representations of minimal conductor can be induced. Some of our results can be interpreted as criteria for a real quadratic field to be contained in a Galois extension of Q with controlled ramification and Galois group isomorphic to a generalized quaternion group.