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February 2006 Lattice counting for deformations of convex domains
Yiannis N. Petridis, John A. Toth
J. Differential Geom. 72(2): 339-352 (February 2006). DOI: 10.4310/jdg/1143593212

Abstract

Let D0 = {x ∈ Rn,H0(x) ≤ 1} be a strictly convex domain in Rn with n ≤ 3 and Du = {x ∈ Rn,Hu(x) ≤ 1}, u ∈ [η, η] be a continuous one-parameter deformation of D0 with lattice-point counting function Nu(T) := {m ∈ Zn : Hu(m) ≤ T2}. The main result of this paper is an estimate for large values of T of the variation of the counting function, Nu(T), over generic volume-preserving deformations Du.

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Yiannis N. Petridis. John A. Toth. "Lattice counting for deformations of convex domains." J. Differential Geom. 72 (2) 339 - 352, February 2006. https://doi.org/10.4310/jdg/1143593212

Information

Published: February 2006
First available in Project Euclid: 28 March 2006

zbMATH: 1122.58019
MathSciNet: MR2213574
Digital Object Identifier: 10.4310/jdg/1143593212

Rights: Copyright © 2006 Lehigh University

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Vol.72 • No. 2 • February 2006
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