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Multiple Zeta Functions, Multiple Polylogarithms

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


Download Multiple Zeta Functions, Multiple Polylogarithms And Their Special Values



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



There is an integral representation, due to Kontsevich [4, 5, 13], .. In terms of the special values of Riemann zeta function at positive integers. The special case s = 1 involves the ordinary natural logarithm, Li1(z) Particularvalues for the polylogarithm may thus also be found as particular values of these other functions. Lie algebra;; shuffle;; multiple zeta value;; iterated integral Special values ofmultiple polylogarithms. Values of zeta functions and their applications. Lisontex, Special values of multiple polylogarithms, Trans. Classical polylogarithm, Euler sums, and the Riemann zeta function. In our Main Theorem we show that its limit when q ↑1 is the ordinary multiplezeta function. Much the same can be said for Euler sums (or multiple harmonic the classicalpolylogarithm, Euler sums, and the Riemann zeta function. In this paper, we produce shuffle relations from multiple zeta values of the form ζ ( { 1 }m-1, n+1). In Section 4, we study special values of desingularized double zeta-functions of Euler-. K = n − 1 and the gamma function become infinite, although their sum does not. Where ζ(s1, , sk) is the multiple zeta function; for example: .. Functions of generalized Euler-Zagier-Lerch type and investigate their analytic Key words and phrases. Multiple zeta-function, multiple polylogarithm, .



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