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4 papers · 1 filter
q-Multiple Zeta Functions and q-Multiple Polylogarithms
Jianqiang Zhao
We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, r…
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…
Analytic continuation of multiple polylogarithms
Jianqiang Zhao
In this paper we shall define the analytic continuation of the multiple polylogarithms by using Chen's theory of iterated path integrals and compute the monodromy of all multiple l…
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.