{"id":"openai-math/Asymptotically-minimal-maxima-of-real-Littlewood-polynomials","pdf":"https://github.com/openai/math/blob/main/preprints/Asymptotically-minimal-maxima-of-real-Littlewood-polynomials-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Asymptotically-minimal-maxima-of-real-Littlewood-polynomials-September-23-2026","tags":["littlewood-polynomials","merit-factor","analysis"],"score":0,"title":"Asymptotically minimal maxima of real Littlewood polynomials","domain":"Real and complex analysis","family":"076","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We prove that the minimum possible maximum modulus on the unit circle of a polynomial with N consecutive real coefficients in $`\\{-1,1\\}`$ is $`(1+o(1))\\sqrt N`$, as N tends to infinity through all integers. This disproves the real-sign analogue of Erdős's fixed relative-gap conjecture. As a consequence, the largest binary merit factor at length N tends to infinity through all integer lengths, disproving Turyn's conjecture.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Real ultraflat Littlewood polynomials and unbounded binary merit factors"}