Year: 2016
Type: article
Abstract: The set of primitive vectors on large spheres in the euclidean space of dimension d⩾3 equidistribute when projected on the unit sphere. We consider here a refinement of this problem concerning the direction of the vector, together with the shape of the lattice in its orthogonal complement. Using unipotent dynamics, we obtained the desired equidistribution result in dimension d⩾6 and in dimension d=4,5 under a mild congruence condition on the square of the radius. The case of d=3 is considered in a separate paper.
DOI: 10.1112/jlms/jdv065
Authors: Menny Aka, Manfred Einsiedler, Uri Shapira
Institutions: ETH Zurich, Technion – Israel Institute of Technology
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1784176754