Abstract Let Z (N) denote the minimum number of zeros in 0, 2 π that a cosine polynomial of the form f₀ (t) =₍ ₀ nt f A (t) = ∑ n ∈ A cos n t can have when A is a finite set of non-negative integers of size ∣ A ∣ = N. It is an old problem of Littlewood to determine Z (N). In this paper, we obtain the lower bound Z (N) ≽ (log log N) (1+ o (1) ) which exponentially improves on the previous best bounds of the form Z (N) ≽ (log log log N) c due to Erdélyi and Sahasrabudhe.
Benjamin Bedert (Sun,) studied this question.