论文标题
符号不确定性原理和低度多项式
Sign uncertainty principles and low-degree polynomials
论文作者
论文摘要
我们证明了Bourgain-Clozel-Kahane和Cohn-Gonçalves的渐近版本，因为尺寸倾向于无限。特别是，我们表明，在维度上具有sublinear的程度的多项式无法渐近地改善程度上的多项式。这个问题自然出现在针对球体堆积的线性编程边界和无旋转模块化bootstrap绑定的自由玻色子结合。
We prove an asymptotically sharp version of the Bourgain-Clozel-Kahane and Cohn-Gonçalves sign uncertainty principles for polynomials of sublinear degree times a Gaussian, as the dimension tends to infinity. In particular, we show that polynomials whose degree is sublinear in the dimension cannot improve asymptotically on those of degree at most three. This question arises naturally in the study of both linear programming bounds for sphere packing and the spinless modular bootstrap bound for free bosons.
