Number Theory Home | Number Theory Seminar | ArithmeTexas | Department Home
UIUC
Title:Rank generating functions as weakly holomorphic modular forms
Abstract: Recent works have shown that many enigmatic q-series (for example the "mock theta functions" of Ramanujan) arise as the holomorphic projections of real analytic modular forms. In the 1950s Atkin and Swinnerton-Dyer produced many identities involving the "ranks" of partitions (some of these confirmed conjectures made by Dyson). Recent work of Ono, Bringmann, and Rhoades has explained some of these identities. Using the theory of Maass forms, we produce infinite families of rank generating functions which are in fact holomorphic modular forms; these provide a framework in which to view the identities described above.