On Ray Class Annihilators of Cyclotomic Fields.
Let be a square free integer and . In the present work we determine all the fields such that the -class group, , of is of type or .
For any square-free positive integer with , we prove that the class number of the real cyclotomic field is greater than , where is a primitive th root of unity.
The class numbers h⁺ of the real cyclotomic fields are very hard to compute. Methods based on discriminant bounds become useless as the conductor of the field grows, and methods employing Leopoldt's decomposition of the class number become hard to use when the field extension is not cyclic of prime power. This is why other methods have been developed, which approach the problem from different angles. In this paper we extend one of these methods that was designed for real cyclotomic fields of prime...