Lattice points inside random ellipsoids

Abstract

Let Na(t) = #{tΩa ∩ Zd}, with Ωa = { (a − 2 1 x1, a − 2 2 x2, . . . a − 2 d xd) : x ∈ Ω } , where Ω is the unit ball. Let Ea(t) = Na(t)− t|Ωa|. We give a simple proof of the fact that (*) (∫ 2 1 2 ∫ 2 1 2 · · · ∫ 2 1 2 |Ea(t)|da1da2 . . . dad ) 1 2 / t d−1 2 in 2 and 3 dimensions.

Locations

• The Michigan Mathematical Journal - View - PDF