Mock modular forms and singular combinatorial series

• Autorzy: Amanda Folsom , Susie Kimport
• Języki publikacji: EN

Abstrakty

EN

A celebrated result of Bringmann and Ono shows that the combinatorial rank generating function exhibits automorphic properties after being completed by the addition of a non-holomorphic integral. Since then, automorphic properties of various related combinatorial families have been studied. Here, extending work of Andrews and Bringmann, we study general infinite families of combinatorial q-series pertaining to k-marked Durfee symbols, in which we allow additional singularities. We show that these singular combinatorial families are essentially mixed mock and quasimock modular forms, and provide their explicit non-holomorphic completions. As a special case of our work, we consider k=3, and provide an asymptotic expansion for the associated partition rank statistic, solving a special case of an open problem of Andrews.

Kategorie tematyczne

• 11F37: Forms of half-integer weight; nonholomorphic modular forms
• 11P82: Analytic theory of partitions
• 05A17: Partitions of integers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 159
• Numer: 3
• Strony: 257-297

Daty

wydano

2013

Twórcy

autor

Amanda Folsom

• Mathematics Department, Yale University, 10 Hillhouse Avenue, P.O. Box 208283, New Haven, CT 06520-8283, U.S.A.

autor

Susie Kimport

• Mathematics Department, Yale University, 10 Hillhouse Avenue, P.O. Box 208283, New Haven, CT 06520-8283, U.S.A.

Identyfikatory

DOI

10.4064/aa159-3-4