For every eta > 0 and every sufficiently large integer N, there is a Littlewood polynomial with N consecutive coefficients in {−1,1} whose maximum modulus on the unit circle is at most (1+eta) sqrt(N).
For every eta > 0 and every sufficiently large integer N, there is a Littlewood polynomial with N consecutive coefficients in {−1,1} whose maximum modulus on the unit circle is at most (1+eta) sqrt(N).
For every eta > 0 and every sufficiently large integer N, there is a Littlewood polynomial with N consecutive coefficients in {−1,1} whose maximum modulus on the unit circle is at most (1+eta) sqrt(N).
If correct, proves that the minimum normalized maximum tends to one through all integer lengths, refuting the real-sign fixed-gap conjecture.
Can real-sign Littlewood polynomials approach the Parseval minimum for maximum modulus at every sufficiently large length?
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OpenAI reports asymptotically minimal maxima for real Littlewood polynomials
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