TY - JOUR
T1 - Singular vectors on manifolds and fractals
AU - Kleinbock, Dmitry
AU - Moshchevitin, Nikolay
AU - Weiss, Barak
N1 - Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.
PY - 2021/10
Y1 - 2021/10
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
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AN - SCOPUS:85118308031
SN - 0021-2172
VL - 245
SP - 589
EP - 613
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -