4 papers
On a generalization of a theorem of Popov
Jing-Jing Huang, Huixi Li
In this paper, we obtain sharp estimates for the number of lattice points under and near the dilation of a general parabola, the former generalizing an old result of Popov. We appl…
On two lattice points problems about the parabola
Jing-Jing Huang, Huixi Li
We obtain asymptotic formulae with optimal error terms for the number of lattice points under and near a dilation of the standard parabola, the former improving upon an old result…
Simultaneous approximation on affine subspaces
Jing-Jing Huang, Jason J. Liu
We solve the convergence case of the generalized Baker-Schmidt problem for simultaneous approximation on affine subspaces, under natural diophantine type conditions. In one of our…
Diophantine approximation on the parabola with non-monotonic approximation functions
Jing-Jing Huang
We show that the parabola is of strong Khintchine type for convergence, which is the first result of its kind for curves. Moreover, Jarnik type theorems are established in both the…