document: Dihedral congruence primes and class fields of real quadratic fields 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 / sub + / / sup k-1 / + or-1 where epsilon / sub + / is a totally positive fundamental unit of F . This extends work of Hida . Our results allow us to identify a family of -LRB- ray -RRB- class fields of F which are generated by torsion points on modular abelian varieties
doc_bio_tags: B I I O B I O B I I O O O O O O O O O O B I I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O B I I