Dihedral congruence primes and class fields of real quadratic fields

Brown, Alexander F. ; Ghate, Eknath P. (2002) Dihedral congruence primes and class fields of real quadratic fields Journal of Number Theory, 95 (1). pp. 14-37. ISSN 0022-314X

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1006/jnth.2001.2753

Abstract

We show that for a real quadratic field F the dihedral congruence primes with respect to F for cusp forms of weight k and quadratic nebentypus are essentially the primes dividing expressions of the form εk−1+±1 where ε+ is a totally positive fundamental unit of F. This extends work of Hida. Our results allows us to identify a family of (ray) class fields of F which are generated by torsion points on modular abelian varieties.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Dihedral Congruence Primes; Fundamental Units; Real Quadratic Fields; Class Field Theory
ID Code:101499
Deposited On:09 Mar 2018 10:34
Last Modified:09 Mar 2018 10:34

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