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Combinatorial aspects of multiple zeta values. (English) Zbl 0904.05012

Electron. J. Comb. 5, Research paper R38, 12 p. (1998); printed version J. Comb. 5, 569-580 (1998).
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:

11M32 Multiple Dirichlet series and zeta functions and multizeta values
11M41 Other Dirichlet series and zeta functions
05A19 Combinatorial identities, bijective combinatorics
11Y60 Evaluation of number-theoretic constants