{"id":"openai-math/Almost-everywhere-Fourier-convergence-in-L-log-L","pdf":"https://github.com/openai/math/blob/main/preprints/Almost-everywhere-Fourier-convergence-in-L-log-L-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Almost-everywhere-Fourier-convergence-in-L-log-L-September-23-2026","tags":["harmonic-analysis","fourier-series"],"score":0,"title":"Almost-everywhere Fourier convergence in L log L","domain":"Real and complex analysis","family":"075","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"The $`L\\log L`$ Fourier-convergence conjecture"}