✦ LIBER ✦
Cyclotomic Integers of Prescribed Absolute Value and the Class Group
✍ Scribed by Bernhard Schmidt
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 280 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
We obtain a new method for the study of class groups of cyclotomic fields by investigating cyclotomic integers of prescribed absolute value. Explicit subgroups of the classgroup C modulo the class group C + of the maximal real subfield are exhibited and lower bounds on their orders are derived. For the m th cyclotomic field K m , where m= p a m$, ( p, m$)=1, and p is a prime, we determine the structure of C + C P ÂC + C Q up to a binary parameter; here C P , C Q are the subgroups of C generated by the classes
, and the P i are prime ideals.