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arXiv · 2506.16131

An identity for generating series of deformations of multiple zeta values within an algebraic framework

Yoshihiro Takeyama
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Abstract

Bachmann proves an identity expressing the generating series of MacMahon's generalized sum-of-divisors $q$-series in terms of Eisenstein series. MacMahon's $q$-series can be regarded as a $q$-analogue of the multiple zeta value $\zeta(2, 2, \ldots , 2)$, up to a power of $1-q$. Based on this observation, we generalize Bachmann's identity within an algebraic framework and prove a general identity. As a byproduct, we obtain a formula for the generating series of another deformation of multiple zeta values defined by the author. In this formula, periodlike functions introduced by Lewis and Zagier appear as a counterpart of Eisenstein series.

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Yoshihiro Takeyama. 2025-06-19. An identity for generating series of deformations of multiple zeta values within an algebraic framework. https://arxiv.org/abs/2506.16131

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