Refined class number formulas for $\mathbb{G}_m$
Number Theory
2013-12-17 v1
Abstract
We formulate a generalization of a `refined class number formula' of Darmon. Our conjecture deals with Stickelberger-type elements formed from generalized Stark units, and has two parts: the `order of vanishing' and the `leading term'. Using the theory of Kolyvagin systems we prove a large part of this conjecture when the order of vanishing of the corresponding complex -function is .
Cite
@article{arxiv.1312.4053,
title = {Refined class number formulas for $\mathbb{G}_m$},
author = {Barry Mazur and Karl Rubin},
journal= {arXiv preprint arXiv:1312.4053},
year = {2013}
}