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Dihedral Congruence Primes and Class Fields of Real Quadratic Fields

✍ Scribed by Alexander F. Brown; Eknath P. Ghate

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
234 KB
Volume
95
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 e kΓ€1

ΓΎ AE 1 where e ΓΎ 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.

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