Polynomial bounds for the Chowla Cosine Problem

Benjamin Bedert

Polynomial bounds for the Chowla Cosine Problem

Classical Analysis and ODEs 2025-09-24 v2 Combinatorics Number Theory

Authors: Benjamin Bedert

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.

Cite

@article{arxiv.2509.05260,
  title  = {Polynomial bounds for the Chowla Cosine Problem},
  author = {Benjamin Bedert},
  journal= {arXiv preprint arXiv:2509.05260},
  year   = {2025}
}

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

Polynomial bounds for the Chowla Cosine Problem

Abstract

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