[Submitted on 5 Sep 2025 (v1), last revised 24 Jul 2026 (this version, v3)]

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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.

Submission history

From: Benjamin Bedert [view email]
[v1] Fri, 5 Sep 2025 17:20:01 UTC (15 KB)
[v2] Tue, 23 Sep 2025 13:02:24 UTC (23 KB)
[v3] Fri, 24 Jul 2026 22:50:22 UTC (25 KB)

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