Class numbers in cyclotomic Z_p-extensions
Number Theory
2015-01-05 v4
Abstract
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 refined by new results on class numbers of particular B(p,n), we provide evidence for the following conjecture: For all primes p and positive integers n, the ideal class group of B(p,n) is trivial.
Cite
@article{arxiv.1410.2921,
title = {Class numbers in cyclotomic Z_p-extensions},
author = {John C. Miller},
journal= {arXiv preprint arXiv:1410.2921},
year = {2015}
}
Comments
22 pages. Accepted by the Journal of Number Theory