The L\log L Fourier-convergence conjecture

Proves that the ordinary symmetric Fourier partial sums of every complex-valued function in L\log L(\mathbb T) converge almost everywhere along the full sequence. This resolves the classical sufficiency conjecture at the L\log L scale. (Lean)

Manuscript

Almost-everywhere Fourier convergence in L log L

September 23, 2026 · source · Lean formalization available · cite as \cite{OAI:Almost-everywhere-Fourier-convergence-in-L-log-L-September-23-2026}

We prove that the ordinary symmetric Fourier partial sums of every complex-valued function in L\log L on the circle converge almost everywhere to the function along the full sequence. This establishes the classical L\log L sufficiency conjecture.

Result 075 · Real and complex analysis. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.