Quantum modularity of partial theta series with periodic coefficients
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866913435755741184 |
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| author | Goswami, Ankush Osburn, Robert |
| author_facet | Goswami, Ankush Osburn, Robert |
| contents | We explicitly prove the quantum modularity of partial theta series with even or odd periodic coefficients. As an application, we show that the Kontsevich-Zagier series $\mathscr{F}_t(q)$ which matches (at a root of unity) the colored Jones polynomial for the family of torus knots $T(3,2^t)$, $t \geq 2$, is a weight $3/2$ quantum modular form. This generalizes Zagier's result on the quantum modularity for the "strange" series $F(q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_02457 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Quantum modularity of partial theta series with periodic coefficients Goswami, Ankush Osburn, Robert Number Theory Geometric Topology Quantum Algebra 11F37, 33D15, 57K16 We explicitly prove the quantum modularity of partial theta series with even or odd periodic coefficients. As an application, we show that the Kontsevich-Zagier series $\mathscr{F}_t(q)$ which matches (at a root of unity) the colored Jones polynomial for the family of torus knots $T(3,2^t)$, $t \geq 2$, is a weight $3/2$ quantum modular form. This generalizes Zagier's result on the quantum modularity for the "strange" series $F(q)$. |
| title | Quantum modularity of partial theta series with periodic coefficients |
| topic | Number Theory Geometric Topology Quantum Algebra 11F37, 33D15, 57K16 |
| url | https://arxiv.org/abs/2012.02457 |