6 papers · 1 filter
On the Smallest Counterexample to the Log-Concavity of the D'Arcais Polynomials
Steven Charlton, Bernhard Heim, Johann Stumpenhusen
Recently, Starr used asymptotic methods to disprove a conjecture by Heim--Neuhauser and Abdesselam about the log-concavity of the D'Arcais polynomials, without giving an explicit c…
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.
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…