30 citations · 31 across the 4 of their papers we have counts for
4 papers
Class numbers of large degree nonabelian number fields
Kwang-Seob Kim, John C. Miller
If a number field has a large degree and discriminant, the computation of the class number becomes quite difficult, especially without the assumption of GRH. In this article, we wi…
Class numbers in cyclotomic Z_p-extensions
John C. Miller
For any prime p and any positive integer n, let B(p,n) denote the n-th layer of the cyclotomic Z_p-extension over the rationals. Based on the heuristics of Cohen and Lenstra, and r…
Real cyclotomic fields of prime conductor and their class numbers
John C. Miller
Surprisingly, the class numbers of cyclotomic fields have only been determined for fields of small conductor, e.g. for prime conductors up to 67, due to the problem of finding the…
Class numbers of totally real fields and applications to the Weber class number problem
John C. Miller
The determination of the class number of totally real fields of large discriminant is known to be a difficult problem. The Minkowski bound is too large to be useful, and the root d…