Geodesic
Inhomogeneous Diophantine approximation on curves with non-monotonic error function
Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 2, pp. 164-178

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In this paper we prove a convergent part of inhomogeneous Groshev type theorem for non–degenerate curves in Euclidean space where an error function is not necessarily monotonic. Our result naturally incorporates and generalizes the homogeneous measure theorem for non-degenerate curves. In particular, the method of Inhomogeneous Transference Principle and Sprindzuk's method of essential and inessential domains are used in the proof. 
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     author = {N. V. Budarina},
     title = {Inhomogeneous {Diophantine} approximation on curves with non-monotonic error function},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {164--178},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2013_13_2_a0/}
}
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N. V. Budarina. Inhomogeneous Diophantine approximation on curves with non-monotonic error function. Dalʹnevostočnyj matematičeskij žurnal, Tome 13 (2013) no. 2, pp. 164-178. http://geodesic.mathdoc.fr/item/DVMG_2013_13_2_a0/