Open Access

Quasi-modularity of generalized sum-of-divisors functions

Research in Number Theory20151:18

https://doi.org/10.1007/s40993-015-0019-1

Received: 17 June 2015

Accepted: 5 August 2015

Published: 3 December 2015

Abstract

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.