Littlewood polynomial

Littlewood's problem asks how large the values of such a polynomial must be on the unit circle in the complex plane.

The answer to this would yield information about the autocorrelation of binary sequences.

Littlewood's problem asks for constants c1 and c2 such that there are infinitely many Littlewood polynomials pn , of increasing degree n satisfying for all

The Rudin–Shapiro polynomials provide a sequence satisfying the upper bound with

In 2019, an infinite family of Littlewood polynomials satisfying both the upper and lower bound was constructed by Paul Balister, Béla Bollobás, Robert Morris, Julian Sahasrabudhe, and Marius Tiba.

Roots of all the Littlewood polynomials of degree 15.
An animation showing the roots of all Littlewood polynomials with degree 1 through 14, one degree at a time.