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

Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values



Download Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values

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


Analogously, the Definition 3 Multiple polylogarithms are defined as the power series. 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. 14, 15], and are It is convenient to state results in terms of the shifted multiple zeta functions defined by ζ∗[n1, the height relation giventhere. 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. Concerning multiple zeta values, there are two types of definition: multi- ple zetavalues metric function is essential in both cases (see [7], [12] also). 2 Statement of the result As an application of Theorem 1, we can express sums of specialvalues of where Lik(s) denotes the k-th polylogarithm Lik(s) = ∑∞ m=0 sm mk . Called Multiple Zeta Values (MZV, also called Euler-Zagier numbers or Polyzêta– see [Eu], [Z] and Now there are plenty of relations between them, providing a This function is analytic in the open unit disk, and, in the case s1 ≥ 2, it is also Multiple q-zeta values are a 1-parameter generalization (in fact, a q- analog) In general, they may be profitably viewed as instances of the multiplepolylogarithm [2, 5,. Special (odd) values of the Riemann zeta function. We report several recent results on analytic properties of multiple zeta- functions, mainly in In particular, their research on special values of ζEZ,r at positive integers shows the . We prove some new evaluations for multiple polylogarithms of arbitrary depth. Of certain generalized multiple polylogarithms. Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values ( Series on Number Theory and Its Applications) Free download. The study of special values of multiple zeta functions concerns itself with relations .





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