q-analogues of multiple zeta values and the formal double Eisenstein space

In this survey article, we discuss the algebraic structure of q-analogues of multiple zeta values, which are closely related to derivatives of Eisenstein series. Moreover, we introduce the formal double Eisenstein space, which generalizes the formal double zeta space of Gangl, Kaneko, and Zagier. Us...

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Bibliographic Details
Published in:arXiv.org 2021-08
Main Author: Bachmann, Henrik
Format: Article
Language:English
Subjects:
Algebra
Combinatorial analysis
Online Access:Get full text
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Summary:In this survey article, we discuss the algebraic structure of q-analogues of multiple zeta values, which are closely related to derivatives of Eisenstein series. Moreover, we introduce the formal double Eisenstein space, which generalizes the formal double zeta space of Gangl, Kaneko, and Zagier. Using the algebraic structure of q-analogues of multiple zeta values, we will present a realization of this space. As an application, we will obtain purely combinatorial proofs of identities among (quasi-)modular forms.
ISSN:2331-8422