James Leng

activity

20182026

most citedOn finite spacer rank for words and subshifts

2 citations · 2 across the 8 of their papers we have counts for

collaborators

10 papers

math.DS2026

Monochromatic Almost-Pythagorean Quadruples

James Leng, Redmond McNamara, Andreas Mountakis

We prove that for any set $A$ with positive multiplicative upper density, there exist $x$ , $y$ , $z$ and $w$ in $A$ such that $x^{2} + y^{2} w^{2} = z^{2}$ , generalizing a result of Frantzik…

math.NT2026

A new proof of two-color partition regularity of Pythagorean triples

James Leng

We give a new proof that if the natural numbers are colored in two colors, then there exists a monochromatic Pythagorean triple. The proof was found by ChatGPT Astra.

math.NT2023

Efficient equidistribution of periodic nilsequences and applications

James Leng

This is a companion paper to arXiv:2312.10772. We deduce an equidistribution theorem for periodic nilsequences and use this theorem to give two applications in arithmetic combinato…

math.CA2023

The fractal uncertainty principle via Dolgopyat's method in higher dimensions

Aidan Backus, James Leng, Zhongkai Tao

We prove a fractal uncertainty principle with exponent $\frac{d}{2} - δ + ε$ , $ε > 0$ , for Ahlfors--David regular subsets of $R^{d}$ with dimension $δ$ whi…

math.NT2022

Improved quadratic Gowers uniformity for the Möbius function

James Leng

We demonstrate that $∥ μ ∥_{U^{3} ([N])} ≪_{A}^{ineff} lo g^{- A} (N)$ $∥Λ - Λ_{Q} ∥_{U^{3} ([N])} ≪_{A}^{ineff} lo g^{- A} (N)$ for any $A > 0$ where $Λ_{Q}$ is an approxi…

math.NT2022

A Quantitative Bound For Szemerédi's Theorem for a Complexity One Polynomial Progression over $Z / N Z$

James Leng

Let $N$ be a large prime and $P, Q \in Z [x]$ two linearly independent polynomials with $P (0) = Q (0) = 0$ . We show that if a subset $A$ of $Z / N Z$ lacks a…

math.DS2020

Nonsingular transformations that are ergodic with isometric coefficients and not weakly doubly ergodic

Beatrix Haddock, James Leng, Cesar E. Silva

We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist…

math.DS2020★ 2 cited

On finite spacer rank for words and subshifts

Su Gao, Liza Jacoby, William Johnson +4

We define a notion of rank for words and subshifts that we call spacer rank, extending the notion of rank-one symbolic shifts of Gao and Hill. We construct infinite words of each f…

math.CA2020

Moser's Method and Conservative Extensions of Diffeomorphisms

James Leng

This paper shall be concerned with three main results. After a brief recollection of basic symplectic geometry, we prove using Moser's homotopy method a special case of the Strong…

math.DS2018

Non-Rigid Rank-One Infinite Measures on the Circle

Hindy Drillick, Alonso Espinosa-Dominguez, Jennifer N. Jones-Baro +3

For a class of irrational numbers, depending on their Diophantine properties, we construct explicit rank-one transformations that are totally ergodic and not weakly mixing. We clas…

Monochromatic Almost-Pythagorean Quadruples

A new proof of two-color partition regularity of Pythagorean triples

Efficient equidistribution of periodic nilsequences and applications

The fractal uncertainty principle via Dolgopyat's method in higher dimensions

Improved quadratic Gowers uniformity for the Möbius function

A Quantitative Bound For Szemerédi's Theorem for a Complexity One Polynomial Progression over Z/NZ

Nonsingular transformations that are ergodic with isometric coefficients and not weakly doubly ergodic

On finite spacer rank for words and subshifts

Moser's Method and Conservative Extensions of Diffeomorphisms

Non-Rigid Rank-One Infinite Measures on the Circle

A Quantitative Bound For Szemerédi's Theorem for a Complexity One Polynomial Progression over $Z / N Z$