标题： 带有周期系数的部分θ级数的量子模性 显示英文标题

标题： Quantum modularity of partial theta series with periodic coefficients

摘要： 我们明确证明了具有偶数或奇数周期系数的部分θ级数的量子模性。 作为应用，我们证明了Kontsevich-Zagier级数$\mathscr{F}_t(q)$，在单位根处与环面扭结族$T(3,2^t)$，$t \geq 2$的着色琼斯多项式相匹配，是一个权为$3/2$的量子模形式。 这推广了Zagier关于“奇怪”级数$F(q)$的量子模性结果。 显示英文摘要

摘要： 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 $F(q)$.