Proofs of Two Conjectural Identities on Partial Nahm Sums
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912504512249856 |
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| author | Shi, Changsong Wang, Liuquan |
| author_facet | Shi, Changsong Wang, Liuquan |
| contents | Recently, Wang and Zeng investigated modularity of partial Nahm sums and discovered 14 modular families of such sums. They confirmed modularity for 13 families and proposed a conjecture consisting of two Rogers--Ramanujan type identities for the remaining family. We prove these conjectural identities in two steps. First, employing a transformation formula involving two Bailey pairs, we transform the partial Nahm sums into some specific Hecke-type series. Second, using two distinct approaches, we convert these Hecke-type series to the desired modular infinite products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proofs of Two Conjectural Identities on Partial Nahm Sums Shi, Changsong Wang, Liuquan Number Theory Combinatorics 05A30, 11P84, 33D15, 33D45, 11F03, 11F27 Recently, Wang and Zeng investigated modularity of partial Nahm sums and discovered 14 modular families of such sums. They confirmed modularity for 13 families and proposed a conjecture consisting of two Rogers--Ramanujan type identities for the remaining family. We prove these conjectural identities in two steps. First, employing a transformation formula involving two Bailey pairs, we transform the partial Nahm sums into some specific Hecke-type series. Second, using two distinct approaches, we convert these Hecke-type series to the desired modular infinite products. |
| title | Proofs of Two Conjectural Identities on Partial Nahm Sums |
| topic | Number Theory Combinatorics 05A30, 11P84, 33D15, 33D45, 11F03, 11F27 |
| url | https://arxiv.org/abs/2507.20270 |