# Hugh Montgomery

Affiliation: University of Michigan

Email: hlm@umich.edu

Title Of Talk: Littlewood polynomials

Abstract: A Littlewood polynomial is a trigonometric polynomial whose coefficients $c_n$ are $\pm1$ for $n$ in an interval of length $N$, and are otherwise $0$. Such trigonometric polynomials are of interest to analysts, and in signal processing. We survey what is known, what is new, and open questions regarding these intriguing functions, with special attention to the Shapiro polynomials.