Hecke-Rogers type series representation on mock theta functions
This thesis consists of a collection of results related to Ramanujan’s mock θ-functions, with our primary focus on Hecke-Rogers type series representation on these functions. We provide transformation formulas that lead us to a different representation of the third order mock θ- functions. In a sepa...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Final Year Project |
| Language: | English |
| Published: |
Nanyang Technological University
2020
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/139415 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | This thesis consists of a collection of results related to Ramanujan’s mock θ-functions, with our primary focus on Hecke-Rogers type series representation on these functions. We provide transformation formulas that lead us to a different representation of the third order mock θ- functions. In a separate section, we give the proofs for three theorems regarding the Hecke-Rogers double series representation associated with definite quadratic forms. In addition, we will provide the Hecke representation for fifth order mock θ-functions, with greater analysis on the last two functions χ0(q) and χ1(q). We will end off this thesis with some examples involving Hecke-Rogers type representation, including the use of these representations to prove Gauss’s famous result that every integer is the sum of three triangular numbers. |
|---|