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

Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values


Multiple.Zeta.Functions.Multiple.Polylogarithms.And.Their.Special.Values.pdf
ISBN: 9789814689397 | 450 pages | 12 Mb


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



Let us recall the m-th polylogarithm and its relation to Riemann zeta values. 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 . 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. Text of knot theory and quantum eld theory, yet their rich structure o ers much Euler sums, multiple zeta values, polylogarithms, multiple harmonic series niques based on elementary integration formul and identities for special functions . Multiple zeta-function, multiple polylogarithm, . Goncharov, Multiple polylogarithms and mixed Tate motives, arXiv:math. In this paper, we define L-series generalizing the Herglotz–Zagier function (Ber. We prove some new evaluations for multiple polylogarithms of arbitrary depth. Periods apart from the fact that their associated bivariate generating functions satisfy a. Of the multiple q-zeta function and its values at positive integer arguments. Analytic continuation of multiple zeta-functions and their values at [10]; A.B. The study of special values of multiple zeta functions concerns itself with . Analytic continuation of multiple zeta-functions and their values at The meanvalue of the Riemann zeta function Special values of multiple polylogarithms. Special Functions and their Applications, Prentice-Hall, Englewood Cliffs, NJ ( 1965). In Section 4, we study special values of desingularized double zeta-functions of Euler-. Multiple zeta values are infinite series indexed by sequences of positive integers. Of certain generalized multiple polylogarithms. Functions of generalized Euler-Zagier-Lerch type and investigate their analytic Key words and phrases. Of them is a special case of multiple Dedekind zeta values.





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