期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2012
卷号：109
期号：40
页码：16063-16067
DOI：10.1073/pnas.1211964109
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：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.
