Theoretical computer science · Oct 6, 2026

Exact Fourier transforms below nlog⁡nn\log n

Gives a deterministic length-n discrete Fourier transform algorithm using O(n(log⁡n)1−δ)O(n(\log n)^{1-\delta}) operations for every n, with explicit δ=10−13\delta=10^{-13}. The model uses exact complex arithmetic, unrestricted coefficients and a supplied root of unity, and counts scalar preparation and logarithmic-word indexing.

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