8 papers · 1 filter
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…
Bessenrodt--Ono inequalities for -tuples of pairwise commuting permutations
Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser
Let denote the symmetric group. We consider \begin{equation*} N_{\ell}(n) := \frac{\left\vert Hom\left( \mathbb{Z}^{\ell},S_n\right) \right\vert}{n!} \end{equation*} which al…
On a sign-change conjecture of Schlosser and Zhou
Kathrin Bringmann, Bernhard Heim, Ben Kane
In this paper, we investigate the signs changes of Fourier coefficients of infinite products of -series of Rogers--Ramanujan type. In particular, we prove a conjecture made by S…
Inequalities for -regular partitions
Bernhard Heim, Markus Neuhauser
We build upon the work by Bessenrodt and Ono, as well as Beckwith and Bessenrodt concerning the combined additive and multiplicative behavior of the -regular partition functions…
On a mod property of -tuples of pairwise commuting permutations
Abdelmalek Abdesselam, Bernhard Heim, Markus Neuhauser
Let denote the symmetric group of permutations acting on elements. We investigate the double sequence counting the number of tuples of elements o…
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…