Julian Sahasrabudhe, University of Cambridge

Abstract

While every (nice enough) even function f : [−π, π] → C may be uniquely expressed as a cosine series f(θ) = X r∈Z Cr cos(rθ), the relationship between the sequence of coefficients (Cr)r∈Z and the behavior of the function f remains mysterious in many aspects. We discuss a solution to a problem of J.E. Littlewood about the behavior of the zeros of cosine polynomials with coefficients Cr ∈ {0, 1}.