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An application of the $p$-adic analytic class number formula
Published online by Cambridge University Press: 01 June 2016
Abstract
We propose an algorithm to verify the $p$-part of the class number for a number field $K$, provided $K$ is totally real and an abelian extension of the rational field $\mathbb{Q}$, and $p$ is any prime. On fields of degree 4 or higher, this algorithm has been shown heuristically to be faster than classical algorithms that compute the entire class number, with improvement increasing with larger field degrees.
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- © The Author(s) 2016
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