Polynomial bounds for the Chowla Cosine Problem

2025/09/05 by Benjamin Bedert, Bedert, Benjamin
#math.CA #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.2509.05260

Abstract

Let A⊂ N be a finite set of n=|A| positive integers, and consider the cosine sum f_A(x)=∑_{a∈ A}cos ax. We prove that min_x f_A(x)\leqslant -n ^1/5-o(1), thereby establishing polynomial bounds for the Chowla cosine problem.

Citations

• From small eigenvalues to large cuts, and Chowla's cosine problem
• On a Conjecture of Littlewood and Idempotent Measures

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• From small eigenvalues to large cuts, and Chowla's cosine problem

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