# Littlewood polynomial

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In mathematics, a **Littlewood polynomial** is a polynomial all of whose coefficients are +1 or −1.
**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.
They are named for J. E. Littlewood who studied them in the 1950s.

## Definition

A polynomial

is a *Littlewood polynomial* if all the . *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 on the unit circle. The Rudin-Shapiro polynomials provide a sequence satisfying the upper bound with . No sequence is known (as of 2008) which satisfies the lower bound.

## References

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