UNIMODAL SEQUENCES AND "STRANGE" FUNCTIONS: A FAMILY OF QUANTUM MODULAR FORMS

作者：Bringmann Kathrin^*; Folsom Amanda; Rhoades Robert C

来源：Pacific Journal of Mathematics, 2015, 274(1): 1-25.

DOI：10.2140/pjm.2015.274.1

• quantum modular forms
• mock modular forms
• Jacobi forms
• unimodal sequences
• partitions
• asymptotics
• moment generating functions

We construct an infinite family of quantum modular forms from combinatorial rank "moment" generating functions for strongly unimodal sequences. The first member of this family is Kontsevich's "strange" function studied by Zagier. These results rely upon the theory of mock Jacobi forms. As a corollary, we exploit the quantum and mock modular properties of these combinatorial functions in order to obtain asymptotic expansions.

• 出版日期2015-3