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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Dihedral Artin representations and CM fields
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by David E. Rohrlich;
Proc. Amer. Math. Soc. 152 (2024), 3183-3196
DOI: https://doi.org/10.1090/proc/16793
Published electronically: June 5, 2024

Abstract:

For a fixed CM field $K$ with maximal totally real subfield $F$, we consider isomorphism classes of dihedral Artin representations of $F$ which are induced from $K$, distinguishing between those which are “canonically” induced from $K$ and those which are “noncanonically” induced from $K$. The latter can arise only for Artin representations with image isomorphic to the dihedral group of order 8. We show that asymptotically, the number of noncanonically induced isomorphism classes is always comparable to and in some cases exceeds the number of canonically induced ones.
References
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Bibliographic Information
  • David E. Rohrlich
  • Affiliation: Department of Mathematics and Statistics, Boston University, Boston, Massachusetts 02215
  • MR Author ID: 149885
  • ORCID: 0009-0006-2763-4267
  • Email: rohrlich@math.bu.edu
  • Received by editor(s): December 30, 2021
  • Received by editor(s) in revised form: February 17, 2023, and January 7, 2024
  • Published electronically: June 5, 2024
  • Communicated by: Amanda Folsom
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3183-3196
  • MSC (2020): Primary 11R32; Secondary 11R20
  • DOI: https://doi.org/10.1090/proc/16793
  • MathSciNet review: 4767254