The 4-class ranks of quadratic extensions of certain real quadratic fields
โ Scribed by Frank Gerth III
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 628 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let K=Q(-m) be a real quadratic number field. In this article, we find a necessary and sufficient condition for K to admit an unramified quadratic extension with a normal integral basis distinct from K(-&1), provided that the prime 2 splits neither in KรQ nor in Q(-&m)รQ, in terms of a congruence sa
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 kร1 รพ AE 1 where e รพ is a totally positive fundamental unit of F . This extends work of Hida.