Jonathan Hickman

collaborators

5 papers

math.NT2025

Counting rational points near manifolds: a refined estimate, a conjecture and a variant

Jonathan Hickman, Rajula Srivastava, James Wright

Refining an argument of the second author, we improve the known bounds for the number of rational points near a submanifold of $R^{d}$ of intermediate dimension under a natu…

math.CA2025

The Kakeya Conjecture: where does it come from and why is it important?

Jonathan Hickman

Roughly speaking, the Kakeya Conjecture asks to what extent lines which point in different directions can be packed together in a small space. In $R^{2}$ , the problem is relatively…

math.NT2025

Counting integral points near space curves: a Fourier analytic approach

Jonathan Hickman, Rajula Srivastava

We establish upper and lower bounds for the number of integral points which lie within a neighbourhood of a smooth nondegenerate curve in $R^{n}$ for $n \geq 3$ . These estima…

math.CA2025

Improved $L^{p}$ bounds for the strong spherical maximal operator

Jonathan Hickman, Joshua Zahl

We study the $L^{p}$ mapping properties of the strong spherical maximal function, which is a multiparameter generalisation of Stein's spherical maximal function. We show that this op…

math.CA2024

Spherical maximal estimates via geometry

Jonathan Hickman, AjÅ¡a JanÄar

We present a simple geometric approach to studying the $L^{p}$ boundedness properties of Stein's spherical maximal operator, which does not rely on the Fourier transform. Using this,…

Counting rational points near manifolds: a refined estimate, a conjecture and a variant

The Kakeya Conjecture: where does it come from and why is it important?

Counting integral points near space curves: a Fourier analytic approach

Improved Lp bounds for the strong spherical maximal operator

Spherical maximal estimates via geometry

Improved $L^{p}$ bounds for the strong spherical maximal operator