Counting Zeros of Cosine Polynomials: On a Problem of Littlewood

Julian Sahasrabudhe

We show that if $A$ is a finite set of non-negative integers then the number of zeros of the function \[ f_A(θ) = \sum_{a \in A} \cos(aθ), \] in $[0,2\pi ]$, is at least $(\log \log \…