Dihedral congruence primes and class fields of real quadratic fields

JOURNAL OF NUMBER THEORY

卷:95

Article

Brown, AF ; Ghate, EP

关键词: dihedral congruence primes;    fundamental units;    real quadratic fields;    class field theory;   

DOI  :  10.1006/jnth.2001.2753

来源: Elsevier

【 摘 要 】

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 epsilon(1)(k-1) +/-1 where epsilon, 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. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free