Quasi-modularity of generalized sum-of-divisors functions

Quasi-modularity of generalized sum-of-divisors functions

In 1919, P. A. MacMahon studied generating functions for generalized divisor sums. In this paper, we provide a framework in which to view these generating functions in terms of Jacobi forms, and prove that they are quasi-modular forms.

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Veröffentlicht in:Research in number theory 2015-12, Vol.1 (1), Article 18
1. Verfasser: Rose, Simon CF
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Number Theory
Research Article
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Zusammenfassung:In 1919, P. A. MacMahon studied generating functions for generalized divisor sums. In this paper, we provide a framework in which to view these generating functions in terms of Jacobi forms, and prove that they are quasi-modular forms.
ISSN:2363-9555
2363-9555
DOI:10.1007/s40993-015-0019-1