Recursive Formulas for MacMahon and Ramanujan $q$-series
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916500944715776 |
|---|---|
| author | Amdeberhan, Tewodros Barman, Rupam Singh, Ajit |
| author_facet | Amdeberhan, Tewodros Barman, Rupam Singh, Ajit |
| contents | In the present work, we extend current research in a nearly-forgotten but newly revived topic, initiated by P. A. MacMahon, on a generalized notion which relates the divisor sums to the theory of integer partitions and two infinite families of $q$-series by Ramanujan. Our main emphasis will be on explicit representations for a variety of $q$-series, studied primarily by MacMahon and Ramanujan, with an eye towards their modular properties and their proper place in the ring of quasimodular forms of level one and level two. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00262 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recursive Formulas for MacMahon and Ramanujan $q$-series Amdeberhan, Tewodros Barman, Rupam Singh, Ajit Number Theory In the present work, we extend current research in a nearly-forgotten but newly revived topic, initiated by P. A. MacMahon, on a generalized notion which relates the divisor sums to the theory of integer partitions and two infinite families of $q$-series by Ramanujan. Our main emphasis will be on explicit representations for a variety of $q$-series, studied primarily by MacMahon and Ramanujan, with an eye towards their modular properties and their proper place in the ring of quasimodular forms of level one and level two. |
| title | Recursive Formulas for MacMahon and Ramanujan $q$-series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.00262 |