TY - JOUR
T1 - Hausdorff dimensions of very well intrinsically approximable subsets of quadratic hypersurfaces
AU - Fishman, Lior
AU - Merrill, Keith
AU - Simmons, David
N1 - Publisher Copyright:
© 2018, Springer Nature Switzerland AG.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - We prove an analogue of a theorem of Pollington and Velani (Sel Math (N.S.) 11:297–307, 2005), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof incorporates the framework of intrinsic approximation on such hypersurfaces first developed in the authors’ joint work with Kleinbock (Intrinsic Diophantine approximation on manifolds, 2014. arXiv:1405.7650v2) with ideas from work of Kleinbock et al. (Sel Math (N.S.) 10:479–523, 2004).
AB - We prove an analogue of a theorem of Pollington and Velani (Sel Math (N.S.) 11:297–307, 2005), furnishing an upper bound on the Hausdorff dimension of certain subsets of the set of very well intrinsically approximable points on a quadratic hypersurface. The proof incorporates the framework of intrinsic approximation on such hypersurfaces first developed in the authors’ joint work with Kleinbock (Intrinsic Diophantine approximation on manifolds, 2014. arXiv:1405.7650v2) with ideas from work of Kleinbock et al. (Sel Math (N.S.) 10:479–523, 2004).
UR - http://www.scopus.com/inward/record.url?scp=85055265327&partnerID=8YFLogxK
U2 - 10.1007/s00029-018-0446-7
DO - 10.1007/s00029-018-0446-7
M3 - Article
AN - SCOPUS:85055265327
SN - 1022-1824
VL - 24
SP - 3875
EP - 3888
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 5
ER -