Ernie Croot

activity

19992026

most citedProgression-free sets in Z_4^n are exponentially small

94 citations · 124 across the 48 of their papers we have counts for

collaborators

50 papers

math.NT2026

The Prouhet--Tarry--Escott problem for subsets with small doubling in integral domains

Ernie Croot, Junzhe Mao, Chi Hoi Yip

The Prouhet--Tarry--Escott (PTE) problem has many generalizations and has been studied in various algebraic domains. In this paper, we prove that finite subsets $S$ of integral dom…

math.NT2026

A sharp inverse theorem for the quadratic large sieve

Ernie Croot, Chi Hoi Yip, Junzhe Mao +1

We prove that if $A \subseteq [N]$ , $∣ A ∣ ≫ N$ , and $∣ A_{p} ∣ \leq p /2 + O (1)$ for every prime $p ≪ lo g N$ , then $A$ contains at least $exp (c lo g N / lo g lo g N)$ el…

math.NT2026

A combinatorial large sieve for Sidon sets, distances, and norm forms

Ernie Croot, Junzhe Mao, Cosmin Pohoata +2

We develop a new combinatorial large sieve method for sets with bounded algebraic multiplicities. The method exploits algebraic splitting modulo many small primes: local congruence…

math.CO2026

4-cycle-free induced subgraphs of grid graphs

Taiki Aiba, Ernie Croot

The avoidance of induced forests, or induced acyclic subgraphs, in $d$ -dimensional grid graphs, or lattice graphs, has been studied in Alon et al. and later in Caragiannis et al.,…

math.NT2026

Hilbert cubes in sets with arithmetic properties

Ernie Croot, Junzhe Mao, Chi Hoi Yip

In this paper, we introduce new general frameworks for estimating the maximal dimension of Hilbert cubes contained in finite truncations of arbitrary sets. As applications, we inve…

math.NT2025

An inverse theorem on sets with rich additive structure modulo primes

Ernie Croot, Junzhe Mao, Chi Hoi Yip

In this paper, we prove several results on the structure of maximal sets $S \subseteq [N]$ such that $S$ mod $p$ is contained in a short arithmetic progression, or the union of sho…