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[2509.05260] Polynomial bounds for the Chowla Cosine Problem
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[v1] Fri, 5 Sep 2025 17:20:01 UTC (15 KB)
[v2] Tue, 23 Sep 2025 13:02:24 UTC (23 KB)
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Mathematics > Classical Analysis and ODEs
arXiv:2509.05260 (math)
[Submitted on 5 Sep 2025 (v1), last revised 23 Sep 2025 (this version, v2)]
Title:Polynomial bounds for the Chowla Cosine Problem
Authors: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 $$\min_x f_A(x)\leqslant -n^{ 1/7-o(1)},$$ thereby establishing polynomial bounds for the Chowla cosine problem.
| Comments: | 18 pages. New version improves the exponent to 1/7, and proves polynomial bounds for general cosine polynomials with coefficients in an arbitrary finite set |
| Subjects: | Classical Analysis and ODEs (math.CA); Combinatorics (math.CO); Number Theory (math.NT) |
| Cite as: | arXiv:2509.05260 [math.CA] |
| (or arXiv:2509.05260v2 [math.CA] for this version) | |
| https://doi.org/10.48550/arXiv.2509.05260
arXiv-issued DOI via DataCite
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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)
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View a PDF of the paper titled Polynomial bounds for the Chowla Cosine Problem, by Benjamin Bedert
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