activity
20232025
collaborators

6 papers

math.DS2025

Structured extensions and multi-correlation sequences

James Leng

We show that every multi-correlation sequence is the sum of a generalized nilsequence and a null-sequence. This proves a conjecture of N. Frantzikinakis. A key ingredient is the re…

math.NT2024

Vinogradov's theorem for primes with restricted digits

James Leng, Mehtaab Sawhney

Let be sufficiently large, , and be the set of integers with no digit equal to in their base expansion. We prove that every suffic…

math.CO2024

Improved Bounds for Szemerédi's Theorem

James Leng, Ashwin Sah, Mehtaab Sawhney

Let denote the size of the largest subset of with no -term arithmetic progression. We show that for , there exists such that \[r_…

math.CO2024

Quasipolynomial bounds on the inverse theorem for the Gowers -norm

James Leng, Ashwin Sah, Mehtaab Sawhney

We prove quasipolynomial bounds on the inverse theorem for the Gowers -norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input rece…

math.NT2023

Improved bounds for five-term arithmetic progressions

James Leng, Ashwin Sah, Mehtaab Sawhney

Let be the largest cardinality of a set in which does not contain elements in arithmetic progression. Then there exists a constant such t…

math.NT2023

Efficient Equidistribution of Nilsequences

James Leng

We give improved bounds for the equidistribution of (multiparameter) nilsequences subject to any degree filtration. The bounds we obtain are single exponential in dimension, improv…