Relative regulators of number fields
type: Item
instance of: scholarly article
title: Relative regulators of number fields
zbMATH Open document ID: 0945.11022
author: Nils-Peter Skoruppa
author: Eduardo Friedman
published in: Inventiones Mathematicae
publication date: 1999-06-02T00:00:00Z
review text: Let \(L\) be an algebraic number field. \textit{R. Zimmert} [Invent. Math. 62, 367-380 (1980; Zbl 0456.12003)]\ found positive constants \(c_0,c_1\) such that the regulator \(\text{Reg}(L)\) satisfies \[ \text{Reg}(L)\geq c_oc_1^{[L:\mathbb Q]}. \] \textit{A.-M. Bergé} and \textit{J. Martinet} [Sémin. Théor. Nombres, Paris/Fr. 1987-88, Prog. Math. 81, 23-50 (1990; Zbl 0699.12014)]\ defined a relative regulator associated to an extension \(L/K\), which is essentially the ratio \(\text{Reg}(L)/\text{Reg}(K)\). They asked whether a result analogous to that of Zimmert holds for the relative regulator. The present authors derive such a result, i.e., they prove the following Main Theorem: There exist positive absolute constants \(d_0,d_1\) such that for any extension \(L/K\) of number fields we have \[ \text{Reg}(L)/\text{Reg}(K)\geq\big(d_0d_1^{[L:K]}\big)^{[K:\mathbb Q]}. \]
reviewed by: Veikko Ennola
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R47
zbMATH DE Number: 1275786
zbMATH Keywords: relative regulator
zbMATH Keywords: theta series
MaRDI profile type: Publication
full work available at URL: s002220050281
OpenAlex ID: W1978132086
DOI: 10.1007/S002220050281
description: scientific article; zbMATH DE number 1275786