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


Abstract: Multiple zeta values (MZVs) possess a rich algebraic structure of algebraic Instead, all of its periods must be considered, corresponding to convergent . 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,. Analytic continuation of multiple zeta-functions and their values at The meanvalue of the Riemann zeta function Special values of multiple polylogarithms. 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 . Analogously, the Definition 3 Multiple polylogarithms are defined as the power series. 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. Special values of L-series associated to elliptic curves in terms of “elliptic .. Title: Zagier's conjecture on special values of Dedekind zetafunctions. Special (odd) values of the Riemann zeta function. The natural conjecture “lifted zeta-value = lifted polylog value” is supported by the numerical data (cf. Multiple zeta values called “the sum formula” and “the cyclic sum formula” special value of the generating function of multiple polylogarithms [14]. Above complex multiple zeta-functions by showing that the special values of the adic multiple polylogarithm, multiple Bernoulli numbers, multiple Kummer .zeta-function of the generalized Euler-Zagier type (0.1) is its special case, that is,. We prove some new evaluations for multiple polylogarithms of arbitrary depth. Depending only on m, namely the mth classical polylogarithm function. Of certain generalized multiple polylogarithms. Anti-invariant under Gal(F/Q); then L3(ξ+) is a rational multiple (= 1.





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