Abstract
In this paper we will start with one identity of Ramanujan about Lambert series related to modular relations of degree 7 to give some completely new proofs of several important theta functions identities proved by Berndt and Zhang [1994, J. Number Theory 48, 224-242] via the theory of modular forms. This study also yields a simple proof of one important identity of Ramanujan connected with partitions modulo 7. We also derive some new theta-function identities.
| Original language | English |
|---|---|
| Pages (from-to) | 59-75 |
| Number of pages | 17 |
| Journal | Journal of Number Theory |
| Volume | 83 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 2000 |
| Externally published | Yes |
Keywords
- Elliptic functions
- Lambert series
- Modular equation
- Partition
- Theta functions