Harmonic Analysis on Homogeneous Spaces

On q-Analog of Wolstenholme Type Congruences for Multiple Harmonic Sums

Multiple harmonic sums are iterated generalizations of harmonic sums. Recently Dilcher has considered congruences involving q-analogs of these sums in depth one. In this paper we shall study the homogeneous case for arbitrary depth by using generating functions and shuffle relations of the q-analog of multiple harmonic sums. At the end, we also consider some non-homogeneous cases.

调和多项式的瓦ring问题

The Waring Problem of Harmonic Polynomials

本文研究了调和多项式的瓦ring问题，证明其瓦ring秩等于次数，并提供了计算最小瓦ring分解的算法。

New harmonic number identities with applications

We determine the explicit formulas for the sum of products of homogeneous multiple harmonic sums $\sum_{k=1}^n \prod_{j=1}^r H_k(\{1\}^{λ_j})$ when $\sum_{j=1}^r λ_j\leq 5$. We apply these identities to the study of two congruences modulo a power of a prime.