13 papers
Graph Schemes, Graph Series, and Modularity
Kathrin Bringmann, Chris Jennings-Shaffer, Antun Milas
To a simple graph we associate a so-called graph series, which can be viewed as the Hilbert--Poincaré series of a certain infinite jet scheme. We study new -representations and…
Further -series identities and conjectures relating false theta functions and characters
Chris Jennings-Shaffer, Antun Milas
In this short note, a companion of [20], we discuss several families of -series identities in connection to false and mock theta functions, characters of modules of vertex algeb…
On -series identities for false theta series
Chris Jennings-Shaffer, Antun Milas
We prove several infinite families of -series identities for false theta functions and related series. These identities are motivated by considerations of characters of modules…
The Asymptotic Distribution of the Rank for Unimodal Sequences
Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg
We study the asymptotic behavior of the rank statistic for unimodal sequences. We use analytic techniques involving asymptotic expansions in order to prove asymptotic formulas for…
On a Tauberian Theorem of Ingham and Euler-Maclaurin Summation
Kathrin Bringmann, Chris Jennings-Shaffer, Karl Mahlburg
We discuss two theorems in analytic number theory and combinatory analysis that have seen increased use in recent years. A corollary to a Tauberian theorem of Ingham allows one to…
Some -series identities extending work of Andrews, Crippa, and Simon on sums of divisors functions
Kathrin Bringmann, Chris Jennings-Shaffer
In this article we extend a theorem of Andrews, Crippa, and Simon on the asymptotic behavior of polynomials defined by a general class of recursive equations. Here the polynomials…