Cesaro summation by spheres of lattice sums and Madelung constants

对称群上的Cesaro求和与乘性函数

Cesaro summation and multiplicative functions on a symmetric group

本文研究了Cesaro意义下的可和性及其在排列上的乘性函数的均值研究中的应用。

广义Cesàro收敛、根恒等式与黎曼猜想

Generalised Cesaro Convergence, Root Identities and the Riemann Hypothesis

本文扩展了广义Cesàro求和方法，通过余项Cesàro求和定义根恒等式，利用傅里叶理论与余项Cesàro求和建立表达式，针对Gamma函数和黎曼ζ函数探讨根分布及渐进行为，指出μ=-2时根对称性被打破，从而推翻黎曼猜想。

Almost everywhere divergence of spherical harmonic expansions and equivalence of summation methods

We show that there exists an integrable function on the $n$-sphere $(n\ge 2)$, whose Cesàro (C,$\frac{n-1}{2}$) means with respect to the spherical harmonic expansion diverge unboundedly almost everywhere. By studying equivalence theorems, we also obtain the corresponding results for Riesz and Bochner-Riesz means. This extends results of Stein (1961) for flat tori and complements the work of Taibleson (1985) for spheres.

A new summability method for divergent series

The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose prototypical examples include the Abel summation method, the Cesaro means, and Borel summability method. In this paper, we introduce a new summability method for divergent series, and derive an asymptotic expression to its error term. We show that it is both regular and linear, and that it arises quite naturally in the study of local polynomial approximations of analyt…

发散矩阵级数的求和

Summing divergent matrix series

本研究将经典标量级数求和方法推广为完全非交换的矩阵版本，证明其正则性，给出适配的数值算法，可应用于各类矩阵级数并在多个矩阵分析场景中发挥作用。