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- W4313304591 abstract "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,sge 0 }-sum_{r,s<0}right)(-1)^{r+s}x^ry^sq^{abinom{r}{2}+brs+cbinom{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." @default.
- W4313304591 created "2023-01-06" @default.
- W4313304591 creator A5007760336 @default.
- W4313304591 date "2022-12-26" @default.
- W4313304591 modified "2023-09-23" @default.
- W4313304591 title "A general formula for Hecke-type false theta functions" @default.
- W4313304591 doi "https://doi.org/10.48550/arxiv.2212.13236" @default.
- W4313304591 hasPublicationYear "2022" @default.
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