论文标题
具有周期性系数的部分theta系列的量子模块化
Quantum modularity of partial theta series with periodic coefficients
论文作者
论文摘要
我们明确证明了具有均匀或奇异系数的部分theta系列的量子模块。作为一个应用程序，我们表明Kontsevich-Zagier系列$ \ Mathscr {f} _t（q）$，它匹配（以统一的根）匹配（在Unity的根部）colored Jones for Torus结$ t（3,2^t）$，$ t \ geq 2 $的颜色jones polyenmial for torus nongy of torus nongy of torus nonity toy n of。这将Zagier在“奇怪”系列$ f（q）$的量子模块上的结果概括。
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 $F(q)$.
