Erdős Problem #512
Littlewood's conjecture
PROVED LEANdatabase updated 2026-06-22
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
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 \(e(x)=e^{2\pi ix }\)? Littlewood's conjecture, proved independently by Konyagin [Ko81] and McGehee, Pigno, and Smith [MPS81].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/512.Prizenone
Topicsanalysis
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/512
Attempts
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