MacMahon's sums-of-divisors and their connection to multiple Eisenstein series

We give explicit expressions for MacMahon's generalized sums-of-divisors \(q\)-series \(A_r\) and \(C_r\) by relating them to (odd) multiple Eisenstein series. Recently, these sums-of-divisors have been studied in the context of quasimodular forms, vertex algebras, \(N=4\) \(SU(N)\) Super-Yang-...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Author: Bachmann, Henrik
Format: Article
Language:English
Subjects:
Congruences
Yang-Mills theory
Online Access:Get full text
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Summary:We give explicit expressions for MacMahon's generalized sums-of-divisors \(q\)-series \(A_r\) and \(C_r\) by relating them to (odd) multiple Eisenstein series. Recently, these sums-of-divisors have been studied in the context of quasimodular forms, vertex algebras, \(N=4\) \(SU(N)\) Super-Yang-Mills theory, and the study of congruences of partitions. We relate them to a broader mathematical framework and give explicit expressions for both \(q\)-series in terms of Eisenstein series and their odd variants.
ISSN:2331-8422