Zobrazeno 1 - 10
of 602
pro vyhledávání: '"Bringmann, Kathrin"'
In this paper, we investigate the signs changes of Fourier coefficients of infinite products of $q$-series of Rogers--Ramanujan type. In particular, we prove a conjecture made by Schlosser--Zhou pertaining to such sign changes for products of modulus
Externí odkaz:
http://arxiv.org/abs/2406.03453
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 generating functions with a large variety of different modular propert
Externí odkaz:
http://arxiv.org/abs/2403.00635
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 properties and extensions of these. Firstly, we address a question of Ono
Externí odkaz:
http://arxiv.org/abs/2402.08340
Denote by $N_{\ell}(n)$ the number of $\ell$-tuples of elements in the symmetric group $S_n$ with commuting components, normalized by the order of $S_n$. In this paper, we prove asymptotic formulas for $N_\ell(n)$. In addition, general criteria for l
Externí odkaz:
http://arxiv.org/abs/2401.05874
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 sums, and false theta functions.
Comment: 20 pages
Comment: 20 pages
Externí odkaz:
http://arxiv.org/abs/2401.02820
We prove an asymptotic formula for the number of $d$-fold partition diamonds of $n$ and their Schmidt-type counterparts. In order to do so, we study the asymptotic behavior of certain infinite products. We also remark on interesting potential connect
Externí odkaz:
http://arxiv.org/abs/2311.11805
Autor:
Bringmann, Kathrin, Lovejoy, Jeremy
In this paper we study odd unimodal and odd strongly unimodal sequences. We use $q$-series methods to find several fundamental generating functions. Employing the Euler--Maclaurin summation formula we obtain the asymptotic main term for both types of
Externí odkaz:
http://arxiv.org/abs/2308.11556
In this paper, we prove inequalities for ranks, cranks, and partitions among different classes modulo 11. These were conjectured by Borozenets.
Comment: 17 pages, comments welcome
Comment: 17 pages, comments welcome
Externí odkaz:
http://arxiv.org/abs/2308.02327
In this note, we use a variant of the hyperbola method to prove an asymptotic expansion for the summatory function of the number of irreducible $\mathfrak{su}(3)$-representations of dimension $n$. This is a natural companion result to work of Romik,
Externí odkaz:
http://arxiv.org/abs/2308.02319
Autor:
Bridges, Walter, Bringmann, Kathrin
In this paper, we prove that the number of unimodal sequences of size $n$ is log-concave. These are coefficients of a mixed false modular form and have a Rademacher-type exact formula due to recent work of the second author and Nazaroglu on false the
Externí odkaz:
http://arxiv.org/abs/2307.05120