On determining the 4-rank of the ideal class group of a quadratic field
โ Scribed by J.C Lagarias
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 306 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0022-314X
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๐ SIMILAR VOLUMES
In this note we prove an analogue of the classical Riemann-Hurwitz formula for the minus part of the p-rank of S-ideal class groups of algebraic CM-fields. The result is an improvement of Kida's formula for the cyclotomic Z p -extension.
Let k be an imaginary quadratic number field with C k, 2 , the 2-Sylow subgroup of its ideal class group, isomorphic to Zร2Z\_Zร2Z\_Zร2Z. By the use of various versions of the Kuroda class number formula, we improve significantly upon our previous lower bound for |C k 1 , 2 | , the 2-class number of
Let K be a real abelian number field satisfying certain conditions and K n the n th layer of the cyclotomic Z p -extension of K. We study the relation between the p-Sylow subgroup of the ideal class group and that of the unit group module the cyclotomic unit group of K n . We give certain sufficient