Quaternionic Artin representations and nontraditional arithmetic statistics
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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’s work) 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 $\mathbb {Q}$ with controlled ramification and Galois group isomorphic to a generalized quaternion group.References
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Additional Information
- David E. Rohrlich
- Affiliation: Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215
- MR Author ID: 149885
- Email: rohrlich@math.bu.edu
- Received by editor(s): January 16, 2019
- Received by editor(s) in revised form: March 26, 2019
- Published electronically: June 13, 2019
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 8587-8603
- MSC (2010): Primary 11R32; Secondary 11R20
- DOI: https://doi.org/10.1090/tran/7862
- MathSciNet review: 4029705