Higher depth mock theta functions and $q$-hypergeometric series
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916331980324864 |
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| author | Males, Joshua Mono, Andreas Rolen, Larry |
| author_facet | Males, Joshua Mono, Andreas Rolen, Larry |
| contents | In the theory of harmonic Maass forms and mock modular forms, mock theta functions are distinguished examples which arose from $q$-hypergeometric examples of Ramanujan. Recently, there has been a body of work on higher depth mock modular forms. Here, we introduce distinguished examples of these forms which we call higher depth mock theta functions and develop $q$-hypergeometric expressions for them. We provide three examples of mock theta functions of depth two, each arising by multiplying a classical mock theta function with a certain specialization of a universal mock theta function. In addition, we give their modular completions, and relate each to a $q$-hypergeometric series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_04991 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Higher depth mock theta functions and $q$-hypergeometric series Males, Joshua Mono, Andreas Rolen, Larry Number Theory In the theory of harmonic Maass forms and mock modular forms, mock theta functions are distinguished examples which arose from $q$-hypergeometric examples of Ramanujan. Recently, there has been a body of work on higher depth mock modular forms. Here, we introduce distinguished examples of these forms which we call higher depth mock theta functions and develop $q$-hypergeometric expressions for them. We provide three examples of mock theta functions of depth two, each arising by multiplying a classical mock theta function with a certain specialization of a universal mock theta function. In addition, we give their modular completions, and relate each to a $q$-hypergeometric series. |
| title | Higher depth mock theta functions and $q$-hypergeometric series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2101.04991 |