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arXiv · 2509.05260

Polynomial bounds for the Chowla Cosine Problem

Benjamin Bedert
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Abstract

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

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Benjamin Bedert. 2025-09-05. Polynomial bounds for the Chowla Cosine Problem. https://arxiv.org/abs/2509.05260

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