Partitions, multiple zeta values and the q-bracket

We provide a framework for relating certain q -series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q -series are q -analogues of multiple zeta values. By explicitly describing the (regulari...

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Bibliographic Details
Published in:Selecta mathematica (Basel, Switzerland) Switzerland), 2024-02, Vol.30 (1), Article 3
Main Authors: Bachmann, Henrik, van Ittersum, Jan-Willem
Format: Article
Language:English
Subjects:
Functions (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Polynomials
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Summary:We provide a framework for relating certain q -series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q -series are q -analogues of multiple zeta values. By explicitly describing the (regularized) multiple zeta values one obtains as q → 1 , we extend previous results known in this area. Using this together with the fact that other families of functions on partitions, such as shifted symmetric functions, are elements in our space will then give relations among ( q -analogues of) multiple zeta values. Conversely, we will show that relations among multiple zeta values can be ‘lifted’ to the world of functions on partitions, which provides new examples of functions for which the associated q -series are quasimodular.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-023-00893-4