James Leng

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20232025

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math.NT2024

Vinogradov's theorem for primes with restricted digits

James Leng, Mehtaab Sawhney

Let $g$ be sufficiently large, $b \in {0, \dots, g - 1}$ , and $S_{b}$ be the set of integers with no digit equal to $b$ in their base $g$ expansion. We prove that every suffic…

math.NT2023

Improved bounds for five-term arithmetic progressions

James Leng, Ashwin Sah, Mehtaab Sawhney

Let $r_{5} (N)$ be the largest cardinality of a set in ${1, \dots, N}$ which does not contain $5$ elements in arithmetic progression. Then there exists a constant $c \in (0, 1)$ 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…