Equidistribution of primitive rational points on expanding horospheres

Manfred Einsiedler; Shahar Mozes; Nimish Shah; Uri Shapira

doi:10.1112/S0010437X15007605

Equidistribution of primitive rational points on expanding horospheres

Manfred Einsiedler, Shahar Mozes, Nimish Shah, Uri Shapira

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We confirm a conjecture of Marklof regarding the limiting distribution of certain sparse collections of points on expanding horospheres. These collections are obtained by intersecting the expanded horosphere with a certain manifold of complementary dimension and turns out to be of arithmetic nature. This result is then used along the lines suggested by Marklof to give an analogue of a result of Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.

Original language	American English
Pages (from-to)	667-692
Number of pages	26
Journal	Compositio Mathematica
Volume	152
Issue number	4
DOIs	https://doi.org/10.1112/S0010437X15007605
State	Published - 1 Apr 2016

Bibliographical note

Funding Information:
M. E. acknowledges support of SNF grant 200021-127145. S. M. acknowledges the support of ISF grant 1003/11, BSF grant 2010295, and the University of Zurich. N. S. acknowledges the support of NSF grant 1001654. Chaya Fellow U. S., acknowledges the partial support of the Advanced Research Grant 228304 from the European Research Council and ISF grant 357/13.

Publisher Copyright:
© Foundation Compositio Mathematica 2015.

Keywords

Equidistribution
Homogeneous spaces
Shapes of orthogonal lattices

Access to Document

10.1112/S0010437X15007605

Cite this

@article{e38ed0e6671a4550bb8cbf6c7edd83db,

title = "Equidistribution of primitive rational points on expanding horospheres",

abstract = "We confirm a conjecture of Marklof regarding the limiting distribution of certain sparse collections of points on expanding horospheres. These collections are obtained by intersecting the expanded horosphere with a certain manifold of complementary dimension and turns out to be of arithmetic nature. This result is then used along the lines suggested by Marklof to give an analogue of a result of Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.",

keywords = "Equidistribution, Homogeneous spaces, Shapes of orthogonal lattices",

author = "Manfred Einsiedler and Shahar Mozes and Nimish Shah and Uri Shapira",

note = "Funding Information: M. E. acknowledges support of SNF grant 200021-127145. S. M. acknowledges the support of ISF grant 1003/11, BSF grant 2010295, and the University of Zurich. N. S. acknowledges the support of NSF grant 1001654. Chaya Fellow U. S., acknowledges the partial support of the Advanced Research Grant 228304 from the European Research Council and ISF grant 357/13. Publisher Copyright: {\textcopyright} Foundation Compositio Mathematica 2015.",

year = "2016",

month = apr,

day = "1",

doi = "10.1112/S0010437X15007605",

language = "American English",

volume = "152",

pages = "667--692",

journal = "Compositio Mathematica",

issn = "0010-437X",

publisher = "Cambridge University Press",

number = "4",

}

TY - JOUR

T1 - Equidistribution of primitive rational points on expanding horospheres

AU - Einsiedler, Manfred

AU - Mozes, Shahar

AU - Shah, Nimish

AU - Shapira, Uri

N1 - Funding Information: M. E. acknowledges support of SNF grant 200021-127145. S. M. acknowledges the support of ISF grant 1003/11, BSF grant 2010295, and the University of Zurich. N. S. acknowledges the support of NSF grant 1001654. Chaya Fellow U. S., acknowledges the partial support of the Advanced Research Grant 228304 from the European Research Council and ISF grant 357/13. Publisher Copyright: © Foundation Compositio Mathematica 2015.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - We confirm a conjecture of Marklof regarding the limiting distribution of certain sparse collections of points on expanding horospheres. These collections are obtained by intersecting the expanded horosphere with a certain manifold of complementary dimension and turns out to be of arithmetic nature. This result is then used along the lines suggested by Marklof to give an analogue of a result of Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.

AB - We confirm a conjecture of Marklof regarding the limiting distribution of certain sparse collections of points on expanding horospheres. These collections are obtained by intersecting the expanded horosphere with a certain manifold of complementary dimension and turns out to be of arithmetic nature. This result is then used along the lines suggested by Marklof to give an analogue of a result of Schmidt regarding the distribution of shapes of lattices orthogonal to integer vectors.

KW - Equidistribution

KW - Homogeneous spaces

KW - Shapes of orthogonal lattices

UR - http://www.scopus.com/inward/record.url?scp=84946781647&partnerID=8YFLogxK

U2 - 10.1112/S0010437X15007605

DO - 10.1112/S0010437X15007605

M3 - Article

AN - SCOPUS:84946781647

SN - 0010-437X

VL - 152

SP - 667

EP - 692

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 4

ER -

Equidistribution of primitive rational points on expanding horospheres

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this