Remark: 076-03. Asymptotically minimal maxima of real Littlewood polynomials

Authors: OpenAI. Family 076.

Title: Asymptotically minimal maxima of real Littlewood polynomials.

Abstract: 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.

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.