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Journal Article

Quantum modularity of partial theta series with periodic coefficients

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Osburn,  Robert
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Goswami, A., & Osburn, R. (2021). Quantum modularity of partial theta series with periodic coefficients. Forum Mathematicum, 33(2), 451-463. doi:10.1515/forum-2020-0201.


Cite as: http://hdl.handle.net/21.11116/0000-0008-66B0-E
Abstract
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 $F(q)$.