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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Quaternionic Artin representations and nontraditional arithmetic statistics


Author: David E. Rohrlich
Journal: Trans. Amer. Math. Soc. 372 (2019), 8587-8603
MSC (2010): Primary 11R32; Secondary 11R20
DOI: https://doi.org/10.1090/tran/7862
Published electronically: June 13, 2019
MathSciNet review: 4029705
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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.


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Additional Information

David E. Rohrlich
Affiliation: Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215
Email: rohrlich@math.bu.edu

DOI: https://doi.org/10.1090/tran/7862
Received by editor(s): January 16, 2019
Received by editor(s) in revised form: March 26, 2019
Published electronically: June 13, 2019
Article copyright: © Copyright 2019 American Mathematical Society