Computation of partial zeta values at \(s=0\) over a totally real cubic field
type: Item
instance of: scholarly article
title: Computation of partial zeta values at \(s=0\) over a totally real cubic field
zbMATH Open document ID: 0847.11065
published in: Journal of Number Theory
publication date: 1996-10-13T00:00:00Z
review text: Let \(\zeta(s, A)= \sum_{{\mathfrak A}\in A} N{\mathfrak A}^{-s}\) be the partial zeta-function associated to a ray ideal class \(A\) in a totally real cubic field. The author develops a computationally feasible method for evaluation of the special value \(\zeta (0, A)\). His approach is based on the (by now classical) method of T. Shintani. According to the author, his key idea is to use the lattice points on the boundary of the convex hull of the totally positive elements in the Minkowski space lattice corresponding to \(A\), in order to construct a ``more amenable'' fundamental domain, with respect to the action of the group of units in the ``ray''. The author gives a few numerical examples, in hope ``to compile and publish a more extensive list of tables in the not too distant future''.
Mathematics Subject Classification ID: 11Y40
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 11R80
Mathematics Subject Classification ID: 11R16
zbMATH DE Number: 874195
zbMATH Keywords: Siegel-Shintani formulae
zbMATH Keywords: partial zeta-function
zbMATH Keywords: ray ideal class
zbMATH Keywords: totally real cubic field
zbMATH Keywords: fundamental domain
author: Mizan R. Khan
reviewed by: B. Z. Moroz
MaRDI profile type: Publication
full work available at URL: jnth.1996.0047
OpenAlex ID: W2069996534
DOI: 10.1006/JNTH.1996.0047
description: scientific article; zbMATH DE number 874195