10 papers · 1 filter
Hurwitz class number relations and mock modular forms
Kathrin Bringmann, Jia-Wei Guo, Ben Kane +2
A classical class number relation of Hurwitz expresses the Fourier coefficients of the product of a unary theta function and the class number generating function. Here, we establis…
A direct proof of Mono-Rolen-Stumpenhusen and new constructions via the Maass raising operators
Kathrin Bringmann, Ben Kane
In this paper, we give a direct conceptual proof of the main result of Mono, Rolen, and Stumpenhusen, using differential operators. More precisely, we realize their functions $ω_{k…
On -congruences for meromorphic modular forms with supersingularity
Kathrin Bringmann, Pavel Guerzhoy, Ben Kane +2
In this paper, we investigate congruences for meromorphic modular forms which have a pole at a single point in the fundamental domain of . For a p…
Strict Log-concavity of -coloured Partitions
Kathrin Bringmann, Ben Kane, Anubhab Pahari +1
In recent years, there has been extensive work on inequalities among partition functions. In particular, Nicolas, and independently DeSalvo--Pak, proved that the partition function…
Asymptotics for the Enumeration of Commuting Matrices over Finite Fields
Kathrin Bringmann, Shane Chern, Johann Franke +1
We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.
A generic approach to proving Turán-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences
Koustav Banerjee, Kathrin Bringmann, Ben Kane
We derive an asymptotic expansion with effective error bound for , counting the number of unimodal sequences of size . We prove that satisfies the higher order Turá…
Vanishing properties of Fourier coefficients of holomorphic -quotients
Kathrin Bringmann, Guoniu Han, Bernhard Heim +1
In this paper, we study vanishing of Fourier coefficients of holomorphic -quotients. We investigate examples of two different types: the first one involves integral weight CM ne…
Sign changes of Fourier coefficients for holomorphic eta-quotients
Kathrin Bringmann, Guoniu Han, Bernhard Heim +1
In this paper we study sign changes of an infinite class of -quotients which are holomorphic modular forms. There is also a relation to Hurwitz class numbers.
Periodic sign changes for weakly holomorphic -quotients
Kathrin Bringmann, Guoniu Han, Bernhard Heim +1
In this paper, we study sign changes of weakly holomorphic modular forms which are given as -quotients. We give representative examples for forms of negative weight, weight zero…
Asymptotics of commuting -tuples in symmetric groups and log-concavity
Kathrin Bringmann, Johann Franke, Bernhard Heim
Denote by the number of -tuples of elements in the symmetric group with commuting components, normalized by the order of . In this paper, we prove as…