Unimodal sequences and quantum and mock modular forms

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 form which is “dual” to the quantum form Zagier constructed from Kontsevich’s “strange” function F ( q ). As a result, we obtain a new representation for a certain generating function for L -values. The series U ( i ; q ) = U (- i ; q ) is a mock modular form, and we use this fact to obtain new congruences for certain enumerative functions.