Showing 2026Show all
3 papers · 1 filter
math.NT2026
Remarks on the Geometry of Sets in with Small Fourier Norm
Alex Burgin, Junzhe Mao
We study geometric inverse problems for finite sets whose Fourier norm, or Wiener norm, \begin{align*} \|A\|:=\int_{\mathbb{T}^d}\Big|\sum_{a\in A}e(a…
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…