 "Littlewood's problem" asks for constants "c"1 and "c"2 such that there are infinitely many Littlewood polynomials "p""n" , of increasing degree "n" satisfying

for all formula_4 on the unit circle.The Rudin–Shapiro polynomials provide a sequence satisfying the upper bound with formula_5.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.