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Polynomial bounds for the Chowla Cosine Problem
Published 5 Sep 2025 in math.CA, math.CO, and math.NT | (2509.05260v1)
Abstract: Let $A\subset \mathbf{N}$ be a finite set of $n=|A|$ positive integers, and consider the cosine sum $f_A(t)=\sum_{a\in A}\cos at$. We prove that there exists an absolute constant $c\geqslant 1/12$ such that $$\min_t f_A(t)\leqslant -Ω(nc),$$ establishing polynomial bounds for the Chowla cosine problem.
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