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An application of the $p$-adic analytic class number formula

Published online by Cambridge University Press:  01 June 2016

Claus Fieker
Affiliation:
Fachbereich Mathematik, Technische Universität Kaiserslautern, Germany email fieker@mathematik.uni-kl.de
Yinan Zhang
Affiliation:
School of Mathematics and Statistics, The University of Sydney, Australia email y.zhang@sydney.edu.au

Abstract

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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.

Type
Research Article
Copyright
© The Author(s) 2016 

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