Erdős Problem #996
OPENdatabase updated 2025-09-07
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Does there exists a positive constant `C` such that for all `f ∈ L²[0,1]` and all lacunary sequences `n`, if `‖f - fₖ‖₂ = O(1 / log log log k ^ C)`, then for almost every `x`, `lim ∑ k ∈ Finset.range N, f (n k • x)) / N = ∫ t, f t ∂t`?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/996.Prizenone
Topicsanalysis
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/996
Attempts
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The live page is OPEN (0 formally logged claimed proofs; Currently working: None), but its discussion has a 27 Apr 2026 comment by Przemek Chojecki saying the problem “was claimed” in the linked prepr
SKIPPED