A dimension conjecture for q-analogues of multiple zeta values

Bachmann, Henrik; Kuehn, Ulf

doi:10.1007/978-3-030-37031-2_8

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A dimension conjecture for q-analogues of multiple zeta values

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Bachmann, Henrik
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/978-3-030-37031-2_8
(Publisher version)

https://doi.org/10.48550/arXiv.1708.07464
(Preprint)

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Citation

Bachmann, H., & Kuehn, U. (2020). A dimension conjecture for q-analogues of multiple zeta values. In J. I. Burgos Gil, K. Ebrahimi-Fard, & H. Gangl (Eds.), Periods in quantum field theory and arithmetic: CMAT, Madrid, Spain, September 15 – December 19, 2014 (pp. 237-258). Cham: Springer.

Cite as: https://hdl.handle.net/21.11116/0000-0006-BB7C-D

Abstract

We study a class of q-analogues of multiple zeta values given by certain
formal q-series with rational coefficients. After introducing a notion of
weight and depth for these q-analogues of multiple zeta values we present
dimension conjectures for the spaces of their weight- and depth-graded parts,
which have a similar shape as the conjectures of Zagier and Broadhurst-Kreimer
for multiple zeta values.