Littlewood polynomial

Definition

A polynomial

: p(x) = \sum_{i=0}^n a_i x^i ,

is a Littlewood polynomial if all the .

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

:c_1 \sqrt{n+1} \le | p_n(z) | \le c_2 \sqrt{n+1} . ,

for all z on the unit circle. 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.

References