On a function related to Chowla's cosine problem

Abstract

There is a rich literature that concerns the minimum value of expressions of the form cos a 1 θ + • • • + cos a n θ (where a 1 < • • • < a n are positive integers) and the question of what choice of {a 1 , . . . , a n } maximizes that minimum. A related problem concerns the maximum minimum (on the unit circle) of expressions of the formthen one can ask either for bounds on the functions λ(n) or µ(n), or particular values of λ(n) or µ(n). Other authors have found the values of µ(3) and µ(4). In this paper, we find the values of λ(2) and λ(3).