Geodesic
Combinatorial aspects of multiple zeta values
The electronic journal of combinatorics, Tome 5 (1998)
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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.
DOI : 10.37236/1376
Classification : 11M32, 11M41, 05A19, 11Y60
Mots-clés : Euler sums, Zagier sums, factorial identities, shuffle algebra, Riemann zeta function, Zagier's identity 
@article{10_37236_1376,
     author = {Jonathan M. Borwein and David M. Bradley and David J. Broadhurst and Petr Lison\v{e}k},
     title = {Combinatorial aspects of multiple zeta values},
     journal = {The electronic journal of combinatorics},
     year = {1998},
     volume = {5},
     doi = {10.37236/1376},
     zbl = {0904.05012},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1376/}
}
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Jonathan M. Borwein; David M. Bradley; David J. Broadhurst; Petr Lisoněk. Combinatorial aspects of multiple zeta values. The electronic journal of combinatorics, Tome 5 (1998). doi: 10.37236/1376

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