C. Yip

activity

20222026

most citedExact values and improved bounds on

k

-neighborly families of boxes

1 citations · 3 across the 13 of their papers we have counts for

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7 papers · 1 filter

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

An absolute bound for generalized Diophantine tuples over polynomial rings

Kin Ming Tsang, Chi Hoi Yip

Let $F$ be an algebraically closed field of characteristic $0$ . Let $k \geq 2$ be an integer, and let $n \in F [x] ∖ {0}$ . We study generalized Diophantine tup…

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.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

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…