The Llog L Fourier-convergence conjecture at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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The $L\log L$ Fourier-convergence conjecture

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	squiggles, limits	Levels:	1
Category:	Real and complex analysis	Lean version:	YES! ✔
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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.

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LEVEL 1 Almost-everywhere Fourier convergence in L log L

released 2026-09-23 | 2 theorems · 19 lemmas · 30 proofs · 31,981 words | PLAY LEVEL 1 » (pdf)

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.

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