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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.24646 |
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| _version_ | 1866914422577954816 |
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| author | Garvan, Frank Nath, Hemjyoti |
| author_facet | Garvan, Frank Nath, Hemjyoti |
| contents | In this paper, we develop a unified method for obtaining and proving $m$-dissections of mock theta functions. Our approach builds upon a transformation formula for Appell--Lerch sums due to Hickerson and Mortenson, which allows these sums to be expressed as linear combinations of Appell--Lerch sums together with suitable theta products. By systematically exploiting this representation, and through extensive symbolic computations carried out in Maple, we derive explicit dissection identities in a direct and effective manner. We focus exclusively on the cases of $2$- and $3$-dissections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24646 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | 2- and 3-Dissections of Second-, Sixth-, and Eighth-Order Mock Theta Functions Garvan, Frank Nath, Hemjyoti Number Theory 11F20, 33D15, 11F27 In this paper, we develop a unified method for obtaining and proving $m$-dissections of mock theta functions. Our approach builds upon a transformation formula for Appell--Lerch sums due to Hickerson and Mortenson, which allows these sums to be expressed as linear combinations of Appell--Lerch sums together with suitable theta products. By systematically exploiting this representation, and through extensive symbolic computations carried out in Maple, we derive explicit dissection identities in a direct and effective manner. We focus exclusively on the cases of $2$- and $3$-dissections. |
| title | 2- and 3-Dissections of Second-, Sixth-, and Eighth-Order Mock Theta Functions |
| topic | Number Theory 11F20, 33D15, 11F27 |
| url | https://arxiv.org/abs/2603.24646 |