8-ranks of Class Groups of Some Imaginary Quadratic Number Fields
β Scribed by Xi Mei Wu; Qin Yue
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2007
- Tongue
- English
- Weight
- 322 KB
- Volume
- 23
- Category
- Article
- ISSN
- 1439-7617
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let F be a quadratic extension of Q and O F the ring of integers in F. A result of Tate enables one to compute the 2-rank of K 2 O F in terms of the 2-rank of the class group. Formulas for the 4-rank of K 2 O F exist, but are more involved. We give upper and lower bounds on the 8-rank of K 2 O F in
We prove that, for each prime p dividing n, every infinite class of Witt equivalent number fields of degree n 2 contains a field with the p-rank of the ideal class group exceeding any given number.
Let k be an imaginary quadratic number field with C k, 2 , the 2-Sylow subgroup of its ideal class group, isomorphic to ZΓ2Z\_ZΓ2Z\_ZΓ2Z. 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