Abstract

Littlewood in his 1968 monograph “Some Problems in Real and Complex Analysis” [12, Problem 22] poses the following research problem, which appears to be still open:

Problem. “If the n_j are integral and all different, what is the lower bound on the number of real zeros of ∑ _j=1^N cos(n_jθ)? Possibly N − 1, or not much less.”

No progress seems to have been made on this in the last half century. We show that this is false.

Authors