Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function f (q), Ramanujan claims that as q approaches an… (More)

Since this series is essentially the reciprocal of Dedekind’s weight 1/2 modular form, this provides another example of an Eulerian series which is a modular form. The literature on such identities… (More)

We show that the rank generating function U(t; q) for strongly unimodal sequences lies at the interface of quantum modular forms and mock modular forms. We use U(−1; q) to obtain a quantum modular… (More)

Ramanujan’s famous deathbed letter to G. H. Hardy concerns the asymptotic properties of modular forms and his so-called mock theta functions. For his mock theta function f(q), he asserts, as q… (More)

We develop a new technique for deriving asymptotic series expansions for moments of combinatorial generating functions that uses the transformation theory of Jacobi forms and “mock” Jacobi forms, as… (More)

If f is a polynomial with all of its roots on the real line, then the roots of the derivative f ′ are more evenly spaced than the roots of f . The same holds for a real entire function of order 1… (More)

Moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms.… (More)

A composition of an integer constrained to have decreasing then increasing parts is called concave. We prove that the generating function for the number of concave compositions, denoted v(q), is a… (More)

We give an asymptotic for the number of strongly unimodal sequences of weight n, denoted u∗(n) with error of size O(n ). The result relies on an identity expressing the generating function for u∗(n)… (More)

In studying the enumerative theory of super characters of the group of upper triangular matrices over a finite field we found that the moments (mean, variance and higher moments) of novel statistics… (More)