Mingfeng Chen

activity

20232026

most citedRational points near planar flat curves

1 citations · 1 across the 6 of their papers we have counts for

collaborators

8 papers

math.NT2026

Counterexamples for Rational Points Near Curves

Mingfeng Chen, Rajula Srivastava, Niclas Technau

Let $δ \in [0, 1/2]$ and $Q \geq 1$ . Given a compact $C^{\infty}$ -curve $C$ in $R^{n}$ , denote by $N_{C} (δ, Q)$ the number of pairs $(\mathbf{a}, q)\in \mat…

math.CA2026

On planar Nikodym-type sets

Alan Chang, Mingfeng Chen, Shaoming Guo +3

Nikodym constructed a measure-zero Borel set in the plane that contains a punctured line segment passing through each point in the unit square. Fenton and Falconer asked whether a…

math.NT2026

Sharp Bounds for Rational Points Near Space Curves

Mingfeng Chen, Andreas Seeger, Rajula Srivastava +1

Let $Q \geq 1$ be large, and $δ \in (0, 1)$ be small. Denote by $C \subset R^{3}$ a sufficiently smooth curve with non-vanishing curvature and torsion. How many rational…

math.CA2025

Restriction and Kakeya maximal estimates in $R^{4}$

Tainara Borges, Tiklung Chan, Mingfeng Chen +3

By combining the planebrush argument of Katz and Zahl \cite{katz21} with the decoupling-incidence method of Wang and Wu \cite{WangWu2024}, we derive new bounds for the Fourier rest…

math.NT2025★ 1 cited

Rational points near planar flat curves

Mingfeng Chen

We establish asymptotic formulas for counting rational points near finite type curves on the plane, generalizing Huang's result.

math.CA2024

Oscillatory integral operators and variable Schrödinger propagators: beyond the universal estimates

Mingfeng Chen, Shengwen Gan, Shaoming Guo +3

We consider a class of Hörmander-type oscillatory integral operators in $R^{n}$ for $n \geq 3$ odd with real analytic phase. We derive weak conditions on the phase which ens…

math.CA2024

The dichotomy of Nikodym sets and local smoothing estimates for wave equations

Mingfeng Chen, Shaoming Guo

We show that Nikodym sets and local smoothing estimates for linear wave equations form a dichotomy: If Nikodym sets for a family of curves exist, then the related maximal operator…

math.CA2023

A multi-parameter cinematic curvature

Mingfeng Chen, Shaoming Guo, Tongou Yang

We state a multi-parameter cinematic curvature condition, and prove $L^{p}$ bounds for related maximal operators. In particular, we verify a local smoothing conjecture of Zahl.