Rohrlich, David E.2022-02-072022-02-072019-06-13D. Rohrlich. "Quaternionic Artin representations and nontraditional arithmetic statistics." Transactions of the American Mathematical Society, Volume 372, Issue 12, pp. 8587 - 8603. https://doi.org/10.1090/tran/78620002-99471088-6850https://hdl.handle.net/2144/43785We 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.pp. 8587 - 8603en-USArticle10.1090/tran/7862491576