Theoretical computer science · Oct 6, 2026

Integer multiplication below $n\log n$

Multiplies two n-bit integers exactly at every input length in deterministic worst-case time

O(n(\log n)^{1-\kappa})

, with

\kappa=2^{-182}

, on one fixed finite-alphabet Turing machine with finitely many one-dimensional tapes. This disproves the Schönhage–Strassen

n\log n

optimality conjecture in the ordinary multitape bit model.

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