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On a lattice point problem arising in the spectral analysis of periodic operators

Part of: Geometry of numbers

Published online by Cambridge University Press:  26 February 2010

Sergei V. Konyagin ,
Maxim M. Skriganov  and
Alexander V. Sobolev
Sergei V. Konyagin
Affiliation:
Moscow Lomonosov State University, Moscow, 119899, Russia, E-mail: konyagin@ok.ru
Maxim M. Skriganov
Affiliation:
Centre for Mathematical Analysis and Its Applications, University of Sussex, Falmer, Brighton, BN1 9QH
Alexander V. Sobolev
Affiliation:
Department of Mathematics, University of Sussex, Falmer, Brighton. BN1 9RF, E-mail: A.V.Sobolev@sussex.ac.uk
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Abstract

Let N(ρ; ω) be the number of points of a d-dimensional lattice Γ. where d≥2, inside a ball of radius ρ centred at the point ω. Denote by (ρ) the number N(ρ; ω) averaged over ω in the elementary cell Ω of the lattice Γ. The main result is the following lower bound for for dimensions d ≅ l(mod 4):

MSC classification

Secondary: 11H06: Lattices and convex bodies
Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 87 - 98
Copyright
Copyright © University College London 2003

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