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8-ranks of class groups of quadratic number fields and their densities

✍ Scribed by Qin Yue

Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2011
Tongue
English
Weight
277 KB
Volume
27
Category
Article
ISSN
1439-7617

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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

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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.