Adelic geometry of numbers and generalized Siegel lemmas
type: Item
instance of: scholarly article
title: Adelic geometry of numbers and generalized Siegel lemmas
zbMATH Open document ID: 1231.11076
author: Éric Gaudron
published in: Manuscripta Mathematica
publication date: 2009-10-23T00:00:00Z
review text: Given a finite dimensional vector space over a number field, a Siegel's Lemma provides an explicit upper bound for a nonzero vector of minimal height. Here the author achieves a similar estimate for a vector which does not belong to a finite union of given proper subspaces. Such questions were already investigated, with a different point of view, by \textit{L.~Fukshansky} [Monatsh. Math. 147, No. 1, 25--41 (2006; Zbl 1091.11024); J. Number Theory 120, No. 1, 13--25 (2006; Zbl 1192.11018)]. The results of the paper under review are stronger. This paper is written in the language of adelic vector bundles; a partial translation in terms of geometry of numbers is given. One of the tools is an adelic variant of a theorem of Henk on the number of lattice points of a centrally convex body in terms of the successive minima of the body [\textit{M. Henk}, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 70, 377--384 (2002; Zbl 1126.11034)].
reviewed by: Michel Waldschmidt
Mathematics Subject Classification ID: 11J68
Mathematics Subject Classification ID: 11H06
Mathematics Subject Classification ID: 11G50
Mathematics Subject Classification ID: 14G40
zbMATH DE Number: 5620123
zbMATH Keywords: Siegel's lemma
zbMATH Keywords: adelic geometry of numbers
zbMATH Keywords: lattice points
zbMATH Keywords: successive minima
zbMATH Keywords: minimal vectors
zbMATH Keywords: adelic fibre bundles
zbMATH Keywords: adelic van der Corput inequality
MaRDI profile type: Publication
full work available at URL: s00229-009-0282-3
OpenAlex ID: W2076239889
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DOI: 10.1007/S00229-009-0282-3
description: scientific article; zbMATH DE number 5620123