8 papers
The Jensen--Pólya program and inequalities for arithmetic sequences
Koustav Banerjee, Kathrin Bringmann, Larry Rolen
We develop an analytic framework to study hyperbolicity of Jensen polynomials and related inequalities for arithmetic sequences with general asymptotic growth. Our results provide…
Proof of a conjecture of Andrews and El Bachraoui on the parity of two-color partitions
Koustav Banerjee, Kathrin Bringmann
In this paper, we prove a conjecture of Andrews and El Bachraoui concerning the parity of certain two-color partitions. Precisely, we show that if the Fourier coefficient …
Ramanujan's and Lim's Identities and Harmonic Maass--Jacobi Forms
Kathrin Bringmann, Rajat Gupta, Badri Vishal Pandey
We study an extension of Ramanujan's identities for odd zeta values by Lim and introduce Jacobi analogues of classical Eichler integrals of Eisenstein series. In negative weight we…
Proof of a conjecture of Andrews and Bachraoui on a Hecke sum
Koustav Banerjee, Kathrin Bringmann
In this paper, we prove a conjecture of Andrews and Bachraoui relating a generating function arising from two-color partitions (with odd smallest part and restrictions on the even…
On congruence conjectures of Andrews and Bachraoui
Koustav Banerjee, Kathrin Bringmann, Mohamed El Bachraoui
Andrews and the third author recently studied congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan-type congruences and a vanishing iden…
On a conjecture of Andrews and Bachraoui
Koustav Banerjee, Kathrin Bringmann, William J. Keith
Recently, Andrews and Bachraoui considered a generating function associated with certain two-color partitions, and conjectured that this function has non-negative coef…
Restricted Overpartitions and concave compositions: their modularity and asymptotics
Koustav Banerjee, Kathrin Bringmann, Atul Dixit
In this paper we study restricted overpartitions and concave compositions. In several cases the resulting generating functions involve simultaneously modular forms, mock theta func…
On a generating function of Niebur-Poincaré series
Kathrin Bringmann, Jay Jorgenson, Lejla Smajlović
Let be a Fuchsian group of the first kind which has a cusp of width one. In this paper, we first consider a generating function formed with t…