Quaternionic Artin representations and nontraditional arithmetic statistics
Files
Accepted manuscript
Date
2019-06-13
Authors
Rohrlich, David E.
Version
Accepted manuscript
OA Version
Citation
D. 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/7862
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.