Bailey pairs and quantum $q$-series identites. I. The classical identities
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911176208678912 |
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| author | Dousse, Jehanne Lovejoy, Jeremy |
| author_facet | Dousse, Jehanne Lovejoy, Jeremy |
| contents | We use Bailey pairs to prove $q$-series identities at roots of unity due to Cohen and Bryson-Ono-Pitman-Rhoades. The proofs use Bailey pairs with quadratic forms developed in the study of mock theta functions. In addition to the standard Bailey lemma, we require some changes-of-base established by Bressoud-Ismail-Stanton. We then embed the identities in infinite families using the Bailey chain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bailey pairs and quantum $q$-series identites. I. The classical identities Dousse, Jehanne Lovejoy, Jeremy Number Theory Classical Analysis and ODEs Combinatorics We use Bailey pairs to prove $q$-series identities at roots of unity due to Cohen and Bryson-Ono-Pitman-Rhoades. The proofs use Bailey pairs with quadratic forms developed in the study of mock theta functions. In addition to the standard Bailey lemma, we require some changes-of-base established by Bressoud-Ismail-Stanton. We then embed the identities in infinite families using the Bailey chain. |
| title | Bailey pairs and quantum $q$-series identites. I. The classical identities |
| topic | Number Theory Classical Analysis and ODEs Combinatorics |
| url | https://arxiv.org/abs/2509.21230 |