Inhomogeneous Diophantine approximation on planar curves

TY - JOUR

T1 - Inhomogeneous Diophantine approximation on planar curves

AU - Beresnevich, Victor

AU - Vaughan FRS, Robert

AU - Velani, Sanju

PY - 2011/4

Y1 - 2011/4

N2 - The inhomogeneous metric theory for the set of simultaneously $-approximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous Khintchine-Jarnik type theorems recently established in [Ann. of Math. (2), 166 (2007), pp. 367-426] and [Invent. Math., 166 (2006), pp. 103-124]. The key lies in obtaining essentially the best possible results regarding the distribution of 'shifted' rational points near planar curves.

AB - The inhomogeneous metric theory for the set of simultaneously $-approximable points lying on a planar curve is developed. Our results naturally incorporate the homogeneous Khintchine-Jarnik type theorems recently established in [Ann. of Math. (2), 166 (2007), pp. 367-426] and [Invent. Math., 166 (2006), pp. 103-124]. The key lies in obtaining essentially the best possible results regarding the distribution of 'shifted' rational points near planar curves.

KW - Number Theory

UR - http://www.scopus.com/inward/record.url?scp=79952449759&partnerID=8YFLogxK

U2 - 10.1007/s00208-010-0548-9

DO - 10.1007/s00208-010-0548-9

M3 - Article

SN - 0025-5831

VL - 349

SP - 929

EP - 942

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 4

ER -