AI 中文总结
该研究针对乔拉余弦问题，结合Bedert的估计与加法交集非对称边界的精确平均恒等式，消除亚多项式损失，证明$K(S)\geq c|S|^{1/5}$的无对数下界。
AI 中文摘要
对于正整数的有限集合$S$，记$K(S):=-\min_{x\in\mathbb T}\sum_{s\in S}\cos(2\pi sx)$，Bedert近期证明了一致下界$K(S)\geq |S|^{1/5-o(1)}$。我们消除了亚多项式损失，证明$K(S)\geq c|S|^{1/5}$（$c>0$为绝对常数）。该证明结合了Bedert论证中的两个估计与加法交集非对称边界的精确平均恒等式，此恒等式替代了导致对数损失的乘法放大步骤。
英文摘要
For a finite set $S$ of positive integers, put $K(S):=-\min_{x\in\mathbb T}\sum_{s\in S}\cos(2πsx)$. Bedert recently proved the uniform lower bound $K(S)\geq |S|^{1/5-o(1)}$. We remove the subpolynomial loss and prove that $K(S)\geq c|S|^{1/5}$ for an absolute constant $c>0$. The proof combines two estimates from Bedert's argument with an exact averaging identity for the asymmetric boundaries of additive intersections. This identity replaces the multiplicative-amplification step responsible for the logarithmic loss.
Comments7 pages; ancillary verification script included
