Computation of class numbers by an analytic method
type: Item
instance of: scholarly article
title: Computation of class numbers by an analytic method
zbMATH Open document ID: 0632.12008
DOI: 10.1016/S0747-7171(87)80052-4
author: Carsten Eckhardt
published in: Journal of Symbolic Computation
publication date: 1987-01-01T00:00:00Z
review text: The author develops an analytic method for the computation of the class number h of an algebraic number field F. Using the functional equation of the Dedekind zeta-function he obtains h up to a factor containing R (the regulator of F) as a series expansion. The m-th term of that series involves the number of integral ideals of F of norm m and an integral over a vertical line \(Re(s)>0\). Clearly, it suffices to evaluate the series up to \(m\leq N\) for suitable N so that the remaining part is less than 1/2. The author shows that this can be done effectively. He presents a few impressive examples. Unfortunately the paper does not contain an error analysis so that the described methods will be difficult to be used by other people.
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 12-04
zbMATH DE Number: 4027608
zbMATH Keywords: computation of the class number
zbMATH Keywords: functional equation
zbMATH Keywords: Dedekind zeta- function
zbMATH Keywords: regulator
reviewed by: Michael E. Pohst
MaRDI profile type: Publication
cites work: Q3284027
cites work: Computation of the Class Number and Class Group of a Complex Cubic Field
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cites work: Zur Arithmetik einiger Serien nichtauflösbarer Gleichungen 5. Grades
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description: scientific article; zbMATH DE number 4027608