Ernie Croot

activity

20242026

collaborators

Showing math.NTShow all

6 papers · 1 filter

math.NT2026

A weighted entropy approach for the quadratic inverse large sieve conjecture

Ernie Croot, Chi Hoi Yip

The quadratic inverse large sieve problem predicts that the examples sharp at the square-root threshold are essentially quadratic. Hanson proved the first unconditional result in t…

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.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.NT2026

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…

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 $I^µ > 0$ there are infinitely many integers…