6 papers
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…
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…
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_…
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…
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…
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…