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math.NT2015
Quasi-modularity of generalized sum-of-divisors functions
Simon Rose
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 Jac…
math.NT2014
Introduction to Modular Forms
Simon Rose
We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their app…
math.NT2010
MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms
George E. Andrews, Simon CF Rose
We investigate a relationship between MacMahon's generalized sum-of-divisors functions and Chebyshev polynomials of the first kind. This determines a recurrence relation to compute…