Distribution of shapes of orthogonal lattices
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Date
2019-06
Publication Type
Journal Article
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yes
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Abstract
It was recently shown by Aka, Einsiedler and Shapira that if d > 2, the set of primitive vectors on large spheres when projected to the (d – 1)-dimensional sphere coupled with the shape of the lattice in their orthogonal complement equidistribute in the product space of the sphere with the space of shapes of (d – 1)-dimensional lattices. Specifically, for d = 3, 4, 5 some congruence conditions are assumed. By using recent advances in the theory of unipotent flows, we effectivize the dynamical proof to remove those conditions for d = 4, 5. It also follows that equidistribution takes place with a polynomial error term with respect to the length of the primitive points.
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published
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39 (6)
Pages / Article No.
1531 - 1607
Publisher
Cambridge University Press
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03826 - Einsiedler, Manfred L. / Einsiedler, Manfred L.
03826 - Einsiedler, Manfred L. / Einsiedler, Manfred L.
03826 - Einsiedler, Manfred L. / Einsiedler, Manfred L.
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.