Singular vectors on manifolds and fractals

Dmitry Kleinbock; Nikolay Moshchevitin; Barak Weiss

doi:10.1007/s11856-021-2220-3

Singular vectors on manifolds and fractals

Dmitry Kleinbock, Nikolay Moshchevitin, Barak Weiss

School of Mathematical Sciences

Tel Aviv University

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

Abstract

We generalize Khintchine’s method of constructing totally irrational singular vectors and linear forms. The main result of the paper shows existence of totally irrational vectors and linear forms with large uniform Diophantine exponents on certain subsets of ℝⁿ, in particular on any analytic submanifold of ℝⁿ of dimension ≥2 which is not contained in a proper rational affine subspace.

Original language	American English
Pages (from-to)	589-613
Number of pages	25
Journal	Israel Journal of Mathematics
Volume	245
Issue number	2
DOIs	https://doi.org/10.1007/s11856-021-2220-3
State	Published - 1 Oct 2021

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/s11856-021-2220-3

Cite this

@article{9e0faef877284e02b17c8a93eda81c38,

title = "Singular vectors on manifolds and fractals",

abstract = "We generalize Khintchine{\textquoteright}s method of constructing totally irrational singular vectors and linear forms. The main result of the paper shows existence of totally irrational vectors and linear forms with large uniform Diophantine exponents on certain subsets of ℝn, in particular on any analytic submanifold of ℝn of dimension ≥2 which is not contained in a proper rational affine subspace.",

author = "Dmitry Kleinbock and Nikolay Moshchevitin and Barak Weiss",

note = "Publisher Copyright: {\textcopyright} 2021, The Hebrew University of Jerusalem.",

year = "2021",

month = oct,

day = "1",

doi = "10.1007/s11856-021-2220-3",

language = "American English",

volume = "245",

pages = "589--613",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Singular vectors on manifolds and fractals

AU - Kleinbock, Dmitry

AU - Moshchevitin, Nikolay

AU - Weiss, Barak

PY - 2021/10/1

Y1 - 2021/10/1

N2 - We generalize Khintchine’s method of constructing totally irrational singular vectors and linear forms. The main result of the paper shows existence of totally irrational vectors and linear forms with large uniform Diophantine exponents on certain subsets of ℝn, in particular on any analytic submanifold of ℝn of dimension ≥2 which is not contained in a proper rational affine subspace.

AB - We generalize Khintchine’s method of constructing totally irrational singular vectors and linear forms. The main result of the paper shows existence of totally irrational vectors and linear forms with large uniform Diophantine exponents on certain subsets of ℝn, in particular on any analytic submanifold of ℝn of dimension ≥2 which is not contained in a proper rational affine subspace.

UR - http://www.scopus.com/inward/record.url?scp=85118308031&partnerID=8YFLogxK

U2 - 10.1007/s11856-021-2220-3

DO - 10.1007/s11856-021-2220-3

M3 - Article

SN - 0021-2172

VL - 245

SP - 589

EP - 613

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 2

ER -

Singular vectors on manifolds and fractals

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this