Combinatorial Aspects of Multiple Zeta Values

Borwein, Jonathan M. and Bradley, David M. and Broadhurst, David J. and Lisonek, Petr (1998) Combinatorial Aspects of Multiple Zeta Values. Electronic Journal of Combinatorics, 5 .

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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.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: multiple zeta values, Euler sums, Zagier sums, factorial identities, shuffle algebra
      Subjects: 05-xx Combinatorics > 05Axx Enumerative combinatorics
      11-xx Number theory > 11Mxx Zeta and $L$-functions: analytic theory
      68-xx Computer science > 68Rxx Discrete mathematics in relation to computer science
      11-xx Number theory > 11Yxx Computational number theory
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 28 Nov 2003
      Last Modified: 13 Jan 2015 14:02

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