10 citations · 11 across the 6 of their papers we have counts for
7 papers · 1 filter
On a Problem of Gordon and Hughes: The 11-adic Properties of Meromorphic Modular Functions on
Koustav Banerjee, Nicolas Allen Smoot
Congruence families occur throughout the theory of modular forms. These families superficially resemble one another, though they can vary substantially in their overall difficulty.…
Conguences for Odd Unimodal Sequences and a Problem of Bringmann And Lovejoy
Koustav Banerjee, Manosij Ghosh Dastidar
In this paper, we give a family of the arithmetic progressions in which the numbers of odd unimodal and odd strongly unimodal sequences are divisible by 2 and by 4. In particular,…
Asymptotics for the reciprocal and shifted quotient of the partition function
Koustav Banerjee, Peter Paule, Cristian-Silviu Radu +1
Let denote the partition function. In this paper our main goal is to derive an asymptotic expansion up to order (for any fixed positive integer ) along with estimates…
2-Elongated Plane Partitions and Powers of 7: The Localization Method Applied to a Genus 1 Congruence Family
Koustav Banerjee, Nicolas Allen Smoot
Over the last century, a large variety of infinite congruence families have been discovered and studied, exhibiting a great variety with respect to their difficulty. Major complica…
The Localization Method Applied to -Elongated Plane Partitions and Divisibility by 5
Koustav Banerjee, Nicolas Allen Smoot
The enumeration of -elongated plane partition diamonds has emerged as a generalization of the classical integer partition function . We have discovered an infinit…
New representations for via reciprocity theorems
Koustav Banerjee, Atul Dixit
Two new representations for Ramanujan's function are obtained. The proof of the first one uses the three-variable reciprocity theorem due to Soon-Yi Kang and a transformatio…
Some results on the cubic partition
Prabir Das Adhikary, Koustav Banerjee, Manosij Ghosh Dastidar
In this paper we explore Kruyswijk's method and show how to obtain congruences for cubic partition. That apart we also examine inequalities for a(n) and provide upper bound for it…