Ernie Croot

activity

19992026

most citedSharp Transitions in Making Squares

3 citations · 12 across the 39 of their papers we have counts for

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Showing 2025Show all

3 papers · 1 filter

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…

math.NT2025

Integers with small digits in multiple bases

Thomas F. Bloom, Ernie Croot

We show that, for any $r \geq 1$ , if $g_{1}, \dots, g_{r}$ are distinct coprime integers, sufficiently large depending only on $r$ , then for any $ε > 0$ there are infinitely many integers…

math.NT2025

Diophantine tuples and product sets in shifted powers

Ernie Croot, Chi Hoi Yip

Let $k \geq 2$ and $n \neq = 0$ . A Diophantine tuple with property $D_{k} (n)$ is a set of positive integers $A$ such that $ab + n$ is a $k$ -th power for all $a, b \in A$ with $a \neq = b$ . Such…