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Combinatorial aspects of multiple zeta values. (English) Zbl 0904.05012
Multiple zeta values are nested generalizations of the classical Riemann zeta function evaluated at integer values. In this paper a longstanding conjecture of Don Zagier, together with some generalizations, is proved. Finally computational evidence supporting an infinite family of conjectured generalizations of Zagier’s identity is presented.
MSC:
11M32Multiple Dirichlet series, etc.
11M41Other Dirichlet series and zeta functions
05A19Combinatorial identities, bijective combinatorics
11Y60Evaluation of constants