论文标题
Legendre多项式的符号等级
Sign equidistribution of Legendre polynomials
论文作者
论文摘要
我们证明了Legendre多项式的{\ em标志等级}：区间$ [-1，1] $中区域长度之间的比例，其中legendre polyenmial假定正值和负值，将其收敛到一个程度成长。证明方法还将对称猜想应用于球体中的本征函数。
We prove {\em sign equidistribution} of Legendre polynomials: the ratio between the lengths of the regions in the interval $[-1, 1]$ where the Legendre polynomial assumes positive versus negative values, converges to one as the degree grows. The proof method also has application to the symmetry conjecture for a basis of eigenfunctions in the sphere.
