Méthode du cercle adélique et principe de Hasse fin pour certains systèmes de formes. (Adélic circle method and finite Hasse principle for certain systems of forms)
type: Item
instance of: scholarly article
title: Méthode du cercle adélique et principe de Hasse fin pour certains systèmes de formes. (Adélic circle method and finite Hasse principle for certain systems of forms)
zbMATH Open document ID: 0583.12013
author: Renaud Danset
published in: L'Enseignement Mathématique. 2e Série
publication date: 1985-01-01T00:00:00Z
review text: The circle method of Hardy and Littlewood and a form of Hasse principle are placed in the setting of adèles. The development is based on four hypotheses, the first being related to Weyl's inequality and Dirichlet's theorem on simultaneous rational approximation, and the usual order of dealing with major and minor arcs and the singular series and integral is followed. A special case of the principal theorem of the paper is that when the first two hypotheses are satisfied, the version of the Hasse principle holds for a system of r integral forms of degree d in n variables. The work of Davenport, Birch and Schmidt is discussed from the point of view of this development.
Mathematics Subject Classification ID: 11R56
Mathematics Subject Classification ID: 11P55
Mathematics Subject Classification ID: 11E76
Mathematics Subject Classification ID: 11E04
zbMATH DE Number: 3933187
zbMATH Keywords: Hardy-Littlewood circle method
zbMATH Keywords: system of integral forms
zbMATH Keywords: Hasse principle
zbMATH Keywords: adèles
zbMATH Keywords: simultaneous rational approximation
zbMATH Keywords: singular series
reviewed by: M. M. Dodson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3933187