James Leng

activity

20182026

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

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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.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…

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

Efficient equidistribution of periodic nilsequences and applications

Improved quadratic Gowers uniformity for the Möbius function

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

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