Proof of Two Multivariate $q$-Binomial Sums Arising in Gromov-Witten Theory
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866913539510239232 |
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| author | Krattenthaler, Christian |
| author_facet | Krattenthaler, Christian |
| contents | We prove two multivariate $q$-binomial identities conjectured by Bousseau, Brini and van Garrel [Geom. Topol. 28 (2024), 393-496, arXiv:2011.08830] which give generating series for Gromov-Witten invariants of two specific log Calabi-Yau surfaces. The key identity in all the proofs is Jackson's $q$-analogue of the Pfaff-Saalschütz summation formula from the theory of basic hypergeometric series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_02360 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Proof of Two Multivariate $q$-Binomial Sums Arising in Gromov-Witten Theory Krattenthaler, Christian Classical Analysis and ODEs Algebraic Geometry Combinatorics 33D15, 05A30, 14J32, 14N35, 53D45, 57M27 We prove two multivariate $q$-binomial identities conjectured by Bousseau, Brini and van Garrel [Geom. Topol. 28 (2024), 393-496, arXiv:2011.08830] which give generating series for Gromov-Witten invariants of two specific log Calabi-Yau surfaces. The key identity in all the proofs is Jackson's $q$-analogue of the Pfaff-Saalschütz summation formula from the theory of basic hypergeometric series. |
| title | Proof of Two Multivariate $q$-Binomial Sums Arising in Gromov-Witten Theory |
| topic | Classical Analysis and ODEs Algebraic Geometry Combinatorics 33D15, 05A30, 14J32, 14N35, 53D45, 57M27 |
| url | https://arxiv.org/abs/2102.02360 |