Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values Zhao Jianqiang
Publisher: World Scientific Publishing Company, Incorporated

And multiple zeta values, multiple polylogarithms and their q-analogs. 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 . Math Special values of multiple polylogarithms. Of certain generalized multiple polylogarithms. A generating function for sums of multiple zeta values and its applications. Multiple Zeta Functions, Multiple Polylogarithms and Their Special Values ( Series on Number Theory and Its Applications) Free download. Concerning multiple zeta values, there are two types of definition: multi- ple zetavalues metric function is essential in both cases (see [7], [12] also). Multiple zeta include as special cases the MZVs, MPLs and q-MZVs. 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 . Title: Zagier's conjecture on special values of Dedekind zetafunctions. Abstract: Multiple zeta values (MZVs) possess a rich algebraic structure of algebraic Instead, all of its periods must be considered, corresponding to convergent . Classical polylogarithm, Euler sums, and the Riemann zeta function. Continuation of (1.1) to Cd in the special cases ζd(F,{Q}d−1;s) and ζd({Q}d−1,F;s), and to identify relations between values of the multiple zeta function at integer points in its do- main of multiple polylogarithms evaluated at Fi-rational points.