Jianqiang Zhao

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math.NT2008★ 25 cited

Multiple polylogarithm values at roots of unity

Jianqiang Zhao

For any positive integer $N$ let $μ_{N}$ be the group of the $N$ th roots of unity. In this note we shall study the $\Q$-linear relations among values of multiple polylogarithms evalu…

math.NT2008

Examples of finite $p$ -divisible sets of MHS

Jianqiang Zhao

We provide some examples which give evidence to the conjectures contained in my paper "Finiteness of $p$ -Divisible Sets of Multiple Harmonic Sums" (math.NT/0303043). All the main t…

math.NT2006★ 12 cited

Renormalization of Multiple $q$ -Zeta Values

Jianqiang Zhao

In this paper we shall define the renormalization of the multiple $q$ -zeta values (M $q$ ZV) which are special values of multiple $q$ -zeta functions $ζ_{q} (s_{1}, ..., s_{d})$ when the argum…

math.NT2003

Bernoulli Numbers, Wolstenholme's Theorem, and p^5 Variations of Lucas' Theorem

Jianqiang Zhao

In this note we shall improve some congruences of D.F. Bailey [Two p^3 variations of Lucas' Theorem, JNT 35(1990), pp. 208-215] to higher prime power moduli, by studying the relati…

math.NT2003

Multiple Harmonic Series I: Generalizations of Wolstenholme's Theorem

Jianqiang Zhao

In this paper we will study the p-divisibility of partial sums of multiple zeta value series. In particular we provide some generalizations of the classical Wolstenholme's Theorem.

Multiple polylogarithm values at roots of unity

Examples of finite p-divisible sets of MHS

Renormalization of Multiple q-Zeta Values

Bernoulli Numbers, Wolstenholme's Theorem, and p^5 Variations of Lucas' Theorem

Multiple Harmonic Series I: Generalizations of Wolstenholme's Theorem

Examples of finite $p$ -divisible sets of MHS

Renormalization of Multiple $q$ -Zeta Values