Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 076-01. Ultraflat real Littlewood polynomials
Manuscript map · lines 3965–3974
OpenAI@2026-10-07#rem:oai-p-076-01
Authors: OpenAI. Family 076.
Title: Ultraflat real Littlewood polynomials.
Abstract: For every ${}varepsilon{}in(0,1)$ and every sufficiently large integer N, there is a polynomial of length N with coefficients in ${}{-1,1{}}$ whose modulus lies between $(1-{}varepsilon){}sqrt N$ and $(1+{}varepsilon){}sqrt N$ everywhere on the unit circle. Thus real Littlewood polynomials can be ultraflat through every sufficiently large integer length. The signs may be chosen separately at each length.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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