تقرير
A general formula for Hecke-type false theta functions
| العنوان: | A general formula for Hecke-type false theta functions |
|---|---|
| المؤلفون: | Mortenson, Eric T. |
| المصدر: | Algebra i Analiz 36 (2024), no. 1, 195-203 |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | 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. Comment: The number of pages is perfect. The title has changed |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2212.13236 |
| رقم الأكسشن: | edsarx.2212.13236 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |