Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909274224984064 |
|---|---|
| author | Chen, Rong Zhu, Xiao-Jie |
| author_facet | Chen, Rong Zhu, Xiao-Jie |
| contents | In 2021, Andrews mentioned that George Beck introduced a partition statistic $NT(r,m,n)$ which is related to Dyson's rank statistic. Motivated by Andrews's work, scholars have established a number of congruences and identities involving $NT(r,m,n)$. In this paper, we strengthen and extend a recent work of Mao on the transformation properties of the $NT$ function and provide an analogy of Hickerson and Mortenson's work on the rank function. As an application, we demonstrate how one can deduce from our results many identities involving $NT(r,m,n)$ and another crank-analog statistic $M_ω(r,m,n)$. As a related result, some new properties of generalized Appell-Lerch series are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20790 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series Chen, Rong Zhu, Xiao-Jie Number Theory Combinatorics Primary 11P84, Secondary 05A17, 11F11, 11F30, 11F37, 11P83 In 2021, Andrews mentioned that George Beck introduced a partition statistic $NT(r,m,n)$ which is related to Dyson's rank statistic. Motivated by Andrews's work, scholars have established a number of congruences and identities involving $NT(r,m,n)$. In this paper, we strengthen and extend a recent work of Mao on the transformation properties of the $NT$ function and provide an analogy of Hickerson and Mortenson's work on the rank function. As an application, we demonstrate how one can deduce from our results many identities involving $NT(r,m,n)$ and another crank-analog statistic $M_ω(r,m,n)$. As a related result, some new properties of generalized Appell-Lerch series are given. |
| title | Transformation properties of Andrews-Beck $NT$ functions and generalized Appell-Lerch series |
| topic | Number Theory Combinatorics Primary 11P84, Secondary 05A17, 11F11, 11F30, 11F37, 11P83 |
| url | https://arxiv.org/abs/2407.20790 |