4 papers
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…
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…
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 such that mod is contained in a short arithmetic progression, or the union of sho…
An inverse theorem for generalized arithmetic progression with mild multiplicative property
Ernie Croot, Junzhe Mao
We prove a structural theorem for generalized arithmetic progressions in $\F_p$ which contain a large product set of two other progressions.