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14 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…
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…
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…
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…
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…
Statistics for random representations of Lie algebras
Walter Bridges, Kathrin Bringmann, Caner Nazaroglu
In this paper we investigate how a typical, large-dimensional representation looks for a complex Lie algebra. In particular, we study the family o…
Iterated integrals and cohomology
Kathrin Bringmann, Nikolaos Diamantis
We introduce an extension of the standard cohomology which is characterised by maps that fail to be classical cocycles by products of simpler maps. The construction is motivated by…
Traces of partition Eisenstein series and almost holomorphic modular forms
Kathrin Bringmann, Badri Vishal Pandey
Recently, Amderberhan, Griffin, Ono, and Singh started the study of "traces of partition Eisenstein series" and used it to give explicit formulas for many interesting functions. In…
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…
On the asymptotic behavior for partitions separated by parity
Kathrin Bringmann, William Craig, Caner Nazaroglu
The study of partitions with parts separated by parity was initiated by Andrews in connection with Ramanujan's mock theta functions, and his variations on this theme have produced…
Limiting behaviour and modular completions of MacMahon-like q-series
Kathrin Bringmann, William Craig, Jan-Willem van Ittersum +1
Recently, MacMahon's generalized sum-of-divisor functions were shown to link partitions, quasimodular forms, and q-multiple zeta values. In this paper, we explore many further prop…
Quasi-Jacobi forms, Appell-Lerch functions, and false theta functions as q-brackets of functions on partitions
Kathrin Bringmann, Jan-Willem van Ittersum, Jonas Kaszian
We study certain algebras of theta-like functions on partitions, for which the corresponding generating functions give rise to theta functions, quasi-Jacobi forms, Appell-Lerch sum…
Asymptotics for -fold partition diamonds and related infinite products
Kathrin Bringmann, William Craig, Joshua Males
We prove an asymptotic formula for the number of -fold partition diamonds of and their Schmidt-type counterparts. In order to do so, we study the asymptotic behavior of cert…