4 papers · 1 filter
Depth Two Mock Modularity by Eisenstein Series Coupling
Kathrin Bringmann, Caner Nazaroglu
The notion of depth two and higher mock modular forms have found important applications in mathematical physics and enumerative geometry since their inception through indefinite th…
Asymptotics of partition parts in arithmetic progressions
Kathrin Bringmann, Caner Nazaroglu, Jan-Willem M. van Ittersum
We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying t…
Quasimodularity and Limiting Behavior for Variations of MacMahon Series
Caner Nazaroglu, Badri Vishal Pandey, Ajit Singh
Motivated by the 1920's seminal work of Major MacMahon, Amdeberhan--Andrews--Tauraso recently introduced an infinite family of -series \[ \mathcal{U}_{t}(a;q):= \sum_{1\le n_1<n…
Precision Asymptotics for Partitions Featuring False-Indefinite Theta Functions
Kathrin Bringmann, William Craig, Caner Nazaroglu
Andrews-Dyson-Hickerson, Cohen build a striking relation between q-hypergeometric series, real quadratic fields, and Maass forms. Thanks to the works of Lewis-Zagier and Zwegers we…