A Generalization of the Duality and Sum Formulas on the Multiple Zeta Values
Copyright policy )A Generalization of the Duality and Sum Formulas on the Multiple Zeta Values
The author generalizes a duality theorem of \textit{D. Zagier} [Prog. Math. 120, 497--512 (1994; Zbl 0822.11001)] on multiple zeta values from which several results of \textit{M. Hoffman} [Pac. J. Math. 152, 275--290 (1992; Zbl 0763.11037)] and others are deduced as special cases. Another application is the evaluation of the integral \[ \xi_k(s)= {1\over\Gamma (s)} \int^\infty_0{t^{s-1} \over e^t-1} Li_k(1-e^{-t})\, dt \] for positive integer values of \(s\), where \(Li_k(z)\) denotes the \(k\)th polylogarithm \(\sum^\infty_{m=0} m^{-k}z^m\).
- Osaka University Japan
Algebra and Number Theory, Multiple Dirichlet series and zeta functions and multizeta values, sum formulas, multiple zeta values, polylogarithm, duality theorem
Algebra and Number Theory, Multiple Dirichlet series and zeta functions and multizeta values, sum formulas, multiple zeta values, polylogarithm, duality theorem
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