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



Q-linear forms in the values of the Riemann zeta function at positive integers. The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a Special values of multiple polylogarithms . Multiple zeta values are infinite series indexed by sequences of positive integers. 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 .. 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 . Bibliography of works on multiple zeta values (multiple harmonic series) and Euler sums (values of multiple polylogarithms). Zagier pointed out the connection between multiple zeta values and several . Classical polylogarithm, Euler sums, and the Riemann zeta function. Of certain generalized multiple polylogarithms. Of the multiple q-zeta function and its values at positive integer arguments. Kreimer, Association of multiple zeta values with positive . Tsumura, `Functional relations and special values of Mordell-Tornheim triple zeta and L-functions,' Proc. Values of zeta functions and their applications. Rivoal stated in [30], their hypergeometric identities .. Multiple zeta values called “the sum formula” and “the cyclic sum formula” special value of the generating function of multiple polylogarithms [14].





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