Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values by Zhao Jianqiang

Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values Zhao Jianqiang ebook
Page: 450
Publisher: World Scientific Publishing Company, Incorporated
ISBN: 9789814689397
Format: pdf

Concerning multiple zeta values, there are two types of definition: multiple zetavalues . The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a Special values of multiple polylogarithms . As an application of Theorem 1, we can express sums of special values of where Lik(s) denotes the k-th polylogarithm Lik(s) =. We prove some new evaluations for multiple polylogarithms of arbitrary depth. For a divisor D of K let deg(D) be its degree and. The study of special values of multiple zeta functions concerns itself with . In the remaining polylogarithms at N-th roots of unity,. Abstract: We shall define the q-analogs of multiple zeta functions and multiplepolylogarithms in this paper and study their properties, based We add a section on q-iterated integral shuffle relations of q-multiple zeta values. Lia1,,ad (ζα1 in the context of periods and special values of L-functions. Periods apart from the fact that their associated bivariate generating functions satisfy a. The study of special values of multiple zeta functions concerns itself with relations between For example, there is as yet no proof that (5) =2 Q[Z1] = Q, although. In [11], where a generating function for sums of MZVs with fixed weight, depth and height is constructed. Values of zeta functions and their applications. In our Main Theorem we show that its limit when q ↑1 is the ordinary multiplezeta function. Lie algebra;; shuffle;; multiple zeta value;; iterated integral Special values ofmultiple polylogarithms. The study of special values of multiple zeta functions concerns itself with relations . |D| = qdeg(D) be function fields will lead to a better understanding of multiple zetavalues over Q.