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...
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| Format: | Final Year Project (FYP) |
| Language: | English |
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Nanyang Technological University
2020
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| Online Access: | https://hdl.handle.net/10356/139415 |
| _version_ | 1826114105737478144 |
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| author | Ker, Linus Jian Ting |
| author2 | Chan Song Heng |
| author_facet | Chan Song Heng Ker, Linus Jian Ting |
| author_sort | Ker, Linus Jian Ting |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T03:34:04Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/139415 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:34:04Z |
| publishDate | 2020 |
| publisher | Nanyang Technological University |
| record_format | dspace |
| spelling | ntu-10356/1394152023-02-28T23:12:45Z Hecke-Rogers type series representation on mock theta functions Ker, Linus Jian Ting Chan Song Heng School of Physical and Mathematical Sciences chansh@ntu.edu.sg Science::Mathematics 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. Bachelor of Science in Mathematical Sciences 2020-05-19T07:18:32Z 2020-05-19T07:18:32Z 2020 Final Year Project (FYP) https://hdl.handle.net/10356/139415 en application/pdf Nanyang Technological University |
| spellingShingle | Science::Mathematics Ker, Linus Jian Ting Hecke-Rogers type series representation on mock theta functions |
| title | Hecke-Rogers type series representation on mock theta functions |
| title_full | Hecke-Rogers type series representation on mock theta functions |
| title_fullStr | Hecke-Rogers type series representation on mock theta functions |
| title_full_unstemmed | Hecke-Rogers type series representation on mock theta functions |
| title_short | Hecke-Rogers type series representation on mock theta functions |
| title_sort | hecke rogers type series representation on mock theta functions |
| topic | Science::Mathematics |
| url | https://hdl.handle.net/10356/139415 |
| work_keys_str_mv | AT kerlinusjianting heckerogerstypeseriesrepresentationonmockthetafunctions |