On a function related to Chowla's cosine problem

TL;DR

This paper determines the maximum possible minimum value of sums of cosines with distinct positive integer coefficients for cases when there are two or three terms, advancing understanding of Chowla's cosine problem.

Contribution

The paper explicitly computes the largest minimum of cosine sums for n=2 and n=3, providing exact solutions to a specific case of Chowla's cosine problem.

Findings

Largest minimum for n=2 explicitly computed

Largest minimum for n=3 explicitly computed

Advances understanding of cosine sums with integer coefficients

Abstract

Chowla's cosine problem concerns the largest minimum of an expression of the form $\cos a_1\theta + ... + \cos a_n\theta$ where the $a_i$ are distinct positive integers. We compute this largest minimum when $n$ is 2 or 3.