Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910989265403904 |
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| author | Matsusaka, Toshiki Suzuki, Miyu |
| author_facet | Matsusaka, Toshiki Suzuki, Miyu |
| contents | We extend the recently developed theory of Roehrig and Zwegers on indefinite theta functions to prove certain power series are modular forms. As a consequence, we obtain several power series identities for powers of the generating function of triangular numbers. We also show that these identities arise as specializations of denominator identities of affine Lie superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers Matsusaka, Toshiki Suzuki, Miyu Number Theory Combinatorics 11F27, 17B10 We extend the recently developed theory of Roehrig and Zwegers on indefinite theta functions to prove certain power series are modular forms. As a consequence, we obtain several power series identities for powers of the generating function of triangular numbers. We also show that these identities arise as specializations of denominator identities of affine Lie superalgebras. |
| title | Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers |
| topic | Number Theory Combinatorics 11F27, 17B10 |
| url | https://arxiv.org/abs/2506.04722 |