1 citations · 1 across the 5 of their papers we have counts for
5 papers · 1 filter
On the occurrence of congruence multiplicities between Ramanujan's theta functions
Shane Chern, Nicolas Allen Smoot, Dazhao Tang
Recently, the first and third authors initiated a study of arithmetical relationships between Ramanujan's theta functions and . In this work, we prove eight families…
Explaining Unforeseen Congruence Relationships Between PEND and POND Partitions via an Atkin--Lehner Involution
James A. Sellers, Nicolas Allen Smoot
For the past several years, numerous authors have studied POD and PED partitions from a variety of perspectives. These are integer partitions wherein the odd parts must be distinct…
A Single-Variable Proof of the Omega SPT Congruence Family Over Powers of 5
Nicolas Allen Smoot
In 2018 Liuquan Wang and Yifan Yang proved the existence of an infinite family of congruences for the smallest parts function corresponding to the third order mock theta function $…
A Partition Function Connected with the Göllnitz--Gordon Identities
Nicolas Allen Smoot
We use the celebrated circle method of Hardy and Ramanujan to develop convergent formulae for counting a restricted class of partitions that arise from the Göllnitz--Gordon identit…
A Family of Congruences for Rogers--Ramanujan Subpartitions
Nicolas Allen Smoot
In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, , which counted subpartitions with a structure related to the Rogers--Ramanujan identities. They conje…