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arXiv · 1312.4053

Refined class number formulas for $\mathbb{G}_m$

Barry Mazur·Karl Rubin
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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 $L$-function is $1$.

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Barry Mazur, Karl Rubin. 2013-12-14. Refined class number formulas for $\mathbb{G}_m$. https://arxiv.org/abs/1312.4053

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