论文标题
Hecke型false theta函数的一般公式
A general formula for Hecke-type false theta functions
论文作者
论文摘要
在最近的工作中，Matsusaka概括了Habiro型系列与hikami之后的false theta函数之间的关系，形式的Hecke-type double-sums的五个家族\ begin \ begin {equation*} \ left（\ sum_ sum_ {\ sum_ {r，s \ ge 0 0 } - \ sum_ {r，s <0} \ right）（ - 1）^{r+s} X^ry^sq^sq^{a \ binom {r} {r} {2}+brs+brs+binom {s} s} {s} {2} {2}} {2}} {2}} {2}}，\ end End {equient {equient {equient {equart {equation {equart {equal in $ b^2-ac <0 $ b^2-ac <0 $ b^2-ac <0假theta功能。在这里，我们从theta函数和假theta函数方面获得了此类双重和的通用公式，该函数涵盖了Matsusaka的分解。我们的通用公式在结构上与$ b^2-ac> 0 $相似，在该情况下，Mortenson和Zwegers在Appell功能和Theta功能方面获得了分解。
In recent work where Matsusaka generalizes the relationship between Habiro-type series and false theta functions after Hikami, five families of Hecke-type double-sums of the form \begin{equation*} \left( \sum_{r,s\ge 0 }-\sum_{r,s<0}\right)(-1)^{r+s}x^ry^sq^{a\binom{r}{2}+brs+c\binom{s}{2}}, \end{equation*} where $b^2-ac<0$, are decomposed into sums of products of theta functions and false theta functions. Here we obtain a general formula for such double-sums in terms of theta functions and false theta functions, which subsumes the decompositions of Matsusaka. Our general formula is similar in structure to the case $b^2-ac>0$, where Mortenson and Zwegers obtain a decomposition in terms of Appell functions and theta functions.
