Problem Statement
Is it true that, if $A\subset \mathbb{Z}$ is a finite set of size $N$, then\[\int_0^1 \left\lvert \sum_{n\in A}e(n\theta)\right\rvert \mathrm{d}\theta \gg \log N,\]where $e(x)=e^{2\pi ix }$?
Categories:
Analysis
Progress
Littlewood's conjecture, proved independently by Konyagin [Ko81] and McGehee, Pigno, and Smith [MPS81].Source: erdosproblems.com/512 | Last verified: January 15, 2026