16 citations · 48 across the 10 of their papers we have counts for
10 papers · 1 filter
Extremal affine subspaces and Khintchine-Jarník type theorems
Jing-Jing Huang
We prove a conjecture of Kleinbock which gives a clear-cut classification of all extremal affine subspaces of . We also give an essentially complete classification of…
On the connection between the Goldbach conjecture and the Elliott-Halberstam conjecture
Jing-Jing Huang, Huixi Li
In this paper we prove that the binary Goldbach conjecture for sufficiently large even integers would follow under the assumption that both the Elliott-Halberstam conjecture and a…
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…
The density of rational points near hypersurfaces
Jing-Jing Huang
We establish a sharp asymptotic formula for the number of rational points up to a given height and within a given distance from a hypersurface. Our main innovation is a bootstrap m…
Hausdorff theory of dual approximation on planar curves
Jing-Jing Huang
Ten years ago, Beresnevich-Dickinson-Velani initiated a project that develops the general Hausdorff measure theory of dual approximation on non-degenerate manifolds. In particular,…
Rational points near planar curves and Diophantine approximation
Jing-Jing Huang
In this paper, we establish asymptotic formulae with optimal errors for the number of rational points that are close to a planar curve, which unify and extend the results of Beresn…
A Mean Value Theorem for the Diophantine Equation
Jing-Jing Huang
In this paper, we prove an asymptotic formula for the average number of solutions to the Diophantine equation in which is fixed and and varies.