Counting in generic lattices and higher rank actions

Abstract

We consider the problem of counting lattice points contained in domains in ${\mathbb{R}}^d$ defined by products of linear forms and we show that the normalized discrepancies in these counting problems satisfy non-degenerate Central Limit Theorems, provided that $d\ge 9$. We also study more refined versions pertaining to "spiraling of approximations". Our techniques are dynamical in nature and exploit effective exponential mixing of all orders for actions of higher-rank abelian groups on the space of unimodular lattices.

33 pages, 0 figures, comments are welcome

References in corpus (1)

• Lattice points in large regions and related arithmetic functions: Recent developments in a very classic topic