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



Euler sums, multiple zeta values, polylogarithms, multiple harmonic. Let us recall the m-th polylogarithm and its relation to Riemann zeta values. We state their main combinatorial properties. E uler sums, multiple zeta values, polylogarithms, multiple harmonic series, q uantum fi eld theory, k not theory, R iemann zeta function. Of them is a special case of multiple Dedekind zeta values. Mellin, and then discuss the Euler sum and its multi- variable The problem of analytic continuation of multiple zeta-functions was first con- . 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. Goncharov, Multiple polylogarithms, cyclotomy and modular com-. T he fi rst author sophisticated work relating polylogarithms and their generalizations to arithmetic Techniques based on elementary integration formul e and identities for special func-. K = n − 1 and the gamma function become infinite, although their sum does not. Multivariate zeta function, also called multiple zeta values, multivariate zeta constants (Bailey et al Multivariate zeta functions (and their derivatives) also arise in the D. Special values of multiple polylogarithms. 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. Where ζ(s1, , sk) is the multiple zeta function; for example: .. A generating function for sums of multiple zeta values and its applications. Goncharov, Multiple polylogarithms, cyclotomy and modular complexes Jun-Ichi Okuda, Duality formulas of the special values of multiple polylogarithms, Bull. "Special Values of MultidimensionalPolylogarithms. Series sophisticated work relating polylogarithms and their generalizations to arithmetic niques based on elementary integration formul and identities for specialfunctions. 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 .. The main aim of those papers is the investigation of special values of ζ2(s1,s2) [20] A.





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