Lattice counting for deformations of convex domains

Petridis, Yiannis N.; Toth, John A.

J. Differential Geom., Tome 72 (2006) no. 1, p. 339-352 / Harvested from Project Euclid

Résumé

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

Publié le : 2006-02-14
Classification:

@article{1143593212,
     author = {Petridis, Yiannis N. and Toth, John A.},
     title = {Lattice counting for deformations of convex domains},
     journal = {J. Differential Geom.},
     volume = {72},
     number = {1},
     year = {2006},
     pages = { 339-352},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1143593212}
}

Petridis, Yiannis N.; Toth, John A. Lattice counting for deformations of convex domains. J. Differential Geom., Tome 72 (2006) no. 1, pp.  339-352. http://gdmltest.u-ga.fr/item/1143593212/