$\widetilde{\Xi}_n$ 与 $\widetilde{\Lambda}_n$ 零点的右端点速率
综合数学
2026-04-30 v1
摘要
我们考虑在~\cite{TallaWaffo2026arxiv2602.16761} 中研究的两个偶多项式族 Ξ n \Xi_n Ξ n Λ n \Lambda_n Λ n Ξ ~ n ( x ) : = Ξ n ( x ) \widetilde{\Xi}_n(x):=\Xi_n(\sqrt{x}) Ξ n ( x ) := Ξ n ( x ) Λ ~ n ( x ) : = Λ n ( x ) \widetilde{\Lambda}_n(x):=\Lambda_n(\sqrt{x}) Λ n ( x ) := Λ n ( x ) n ≥ 2 n\ge2 n ≥ 2 ( 0 , 1 ) (0,1) ( 0 , 1 ) 0 < x 1 , n ( Ξ ) < ⋯ < x n − 1 , n ( Ξ ) < 1 0<x^{(\Xi)}_{1,n}<\cdots<x^{(\Xi)}_{n-1,n}<1 0 < x 1 , n ( Ξ ) < ⋯ < x n − 1 , n ( Ξ ) < 1 0 < x 1 , n ( Λ ) < ⋯ < x n − 1 , n ( Λ ) < 1 0<x^{(\Lambda)}_{1,n}<\cdots<x^{(\Lambda)}_{n-1,n}<1 0 < x 1 , n ( Λ ) < ⋯ < x n − 1 , n ( Λ ) < 1 x n − 1 , n ( Ξ ) x^{(\Xi)}_{n-1,n} x n − 1 , n ( Ξ ) x n − 1 , n ( Λ ) x^{(\Lambda)}_{n-1,n} x n − 1 , n ( Λ ) 1 n − 1 log ( 1 − x n − 1 , n ( Λ ) ) → − log 4 , 1 n − 1 log ( 1 − x n − 1 , n ( Ξ ) ) → − log 9. \frac{1}{n-1}\log\bigl(1-x^{(\Lambda)}_{n-1,n}\bigr)\to-\log4, \qquad \frac{1}{n-1}\log\bigl(1-x^{(\Xi)}_{n-1,n}\bigr)\to-\log9. n − 1 1 log ( 1 − x n − 1 , n ( Λ ) ) → − log 4 , n − 1 1 log ( 1 − x n − 1 , n ( Ξ ) ) → − log 9. 1 1 1 Ξ n \Xi_n Ξ n Λ n \Lambda_n Λ n
引用
@article{arxiv.2604.25970,
title = {Right edge rates of the zeros of $\widetilde{\Xi}_n$ and $\widetilde{\Lambda}_n$},
author = {Luc Ramsès Talla Waffo},
journal= {arXiv preprint arXiv:2604.25970},
year = {2026}
}