Corpus ID: 220633458

Multiple zeta values and their q-analogues

@article{Vleeshouwers2020MultipleZV,
  title={Multiple zeta values and their q-analogues},
  author={A. Vleeshouwers},
  journal={arXiv: Number Theory},
  year={2020}
}
We explore the theory of multiple zeta values (MZVs) and some of their $q$-generalisations. Multiple zeta values are numerical quantities that satisfy several combinatorial relations over the rationals. These relations include two multiplicative relations, which arise naturally from comparison of the MZVs with an underlying algebraic structure. We generalise these concepts by introducing the parameter $q$ in such a way that as $q\to 1^-$ we return to the ordinary MZVs. Our special interest lies… Expand

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If n = 1, i = 1 or j = 1, one can easily check see that the equation holds. If i, j > 1, we have Now let us drop the assumption that z s1,r1 z s2,r2 ≡ 0 for all words z s1