10 papers
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…
Eisenstein-type series associated to partition ranks
Kathrin Bringmann, Badri Vishal Pandey, Jan-Willem van Ittersum
In this paper, we introduce a class of functions that behave like classical Eisenstein series in many ways, but with a key distinction: only their non-holomorphic completions trans…
False and partial Eisenstein series related to unimodal sequences
Kathrin Bringmann, Badri Vishal Pandey, Jan-Willem van Ittersum
Motivated by the fact that the classical Jacobi theta function is the exponential generating function of the Eisenstein series, we study the exponential Taylor coeffici…
Ramanujan's partition generating functions modulo
Kathrin Bringmann, William Craig, Ken Ono
For the partition function , Ramanujan proved the striking identities $$ P_5(q):=\sum_{n\geq 0} p(5n+4)q^n =5\prod_{n\geq 1} \frac{\left(q^5;q^5\right)_{\infty}^5}{(q;q)_{\in…
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…
Overpartitions with parts separated by parity
Kathrin Bringmann, Catherine Cossaboom, William Craig
In this paper, we generalize Andrews' partitions separated by parity to overpartitions in two ways. We investigate the generating functions for 16 overpartition families whose part…