A mean value theorem for cubic fields.
type: Item
instance of: scholarly article
title: A mean value theorem for cubic fields.
zbMATH Open document ID: 1053.11082
DOI: 10.1016/S0022-314X(02)00075-6
published in: Journal of Number Theory
publication date: 2003-06-25T00:00:00Z
review text: Das Hauptergebnis besteht in Folgendem: Es bezeichne \(K\) eine kubische Erweiterung des rationalen Zahlkörpers und \(\zeta(s,K)\) die dazugehörige Dedekindsche Zetafunktion. Weiter sei \[ S(x)= \sum_{n\leq x} r(n), \] wenn \(r(n)\) die Anzahl ganzer Ideale der Norm \(n\) in \(K\) bedeutet. Für das Restglied \[ \Delta(x)= S(x)-\alpha x,\quad \alpha= \text{Res}_{s=1}\,\zeta(s, K), \] hat dann das Integral \[ \int^\infty_0 \Delta^2(e^y) e^{-2y\sigma} dy \] die Konvergenzabszisse \(\sigma= {1\over 2}\).
Mathematics Subject Classification ID: 11P21
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11R42
zbMATH DE Number: 1934762
zbMATH Keywords: Gauss lattice point problem
zbMATH Keywords: Dedekind zeta function
zbMATH Keywords: mean value theorem
zbMATH Keywords: integral ideals
zbMATH Keywords: cubic fields
author: Robert C. Vaughan
reviewed by: Ekkehard Krätzel
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1934762