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Quaternionic Artin representations of ℚ

Published online by Cambridge University Press:  09 September 2016

DAVID E. ROHRLICH
DAVID E. ROHRLICH*
Affiliation:
Department of Mathematics and Statistics, Math and Computer Science Building, 111 Cummington Mall Boston University, Boston, MA 02215, U.S.A. e-mail: [email protected]
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Abstract

Isomorphism classes of dihedral Artin representations of ℚ can be counted asymptotically using Siegel's asymptotic averages of class numbers of binary quadratic forms. Here we consider the analogous problem for quaternionic representations. While an asymptotic formula is out of our reach in this case, we show that the asymptotic behaviour in the two cases is quite different.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 1 , July 2017 , pp. 95 - 114
Copyright
Copyright © Cambridge Philosophical Society 2016 

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