Combinatorial aspects of multiple zeta values

Details Combinatorial aspects of multiple zeta values Combinatorial aspects of multiple zeta values

1998-12-02

arxiv.org/abs/math/9812020v1

The Electronic Journal of Combinatorics, Volume 5(1) (1998), R38

Mathematics

Number Theory

12 pages

Scientific paper

Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle product rule allows the possibility of a combinatorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with certain repeated arguments. We also prove a similar cyclic sum identity. Finally, we present extensive computational evidence supporting an infinite family of conjectured MZV identities that simultaneously generalize the Zagier identity.

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