Higher depth quantum modular forms, multiple Eichler integrals, and $frak{sl}_3$ false theta functions.
Higher depth quantum modular forms, multiple Eichler integrals, and $frak{sl}_3$ false theta functions.
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更高深度的量子模形式、多个艾希勒积分和 $frak{sl}_3$ false theta 函数。
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发表时间：
2017
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影响因子：
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通讯作者：
A. Milas
中科院分区：
文献类型：
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作者：
K. Bringmann;Jonas Kaszian;A. Milas
我们介绍和研究更深层次的量子模形式。我们构建了两个家庭的例子来自秩二假θ函数，其“同伴”在下半平面也可以实现为双重Eichler积分和非全纯θ系列的“双误差”函数的值作为系数。特别地，我们证明了出现在顶点代数W^0（p）A_2}$特征标中的frak{sl}_3$的假θ可表示为两个深度为两个正整数权的量子模形式之和.
We introduce and study higher depth quantum modular forms. We construct two families of examples coming from rank two false theta functions, whose "companions" in the lower half-plane can be also realized both as double Eichler integrals and as non-holomorphic theta series having values of "double error" functions as coefficients. In particular, we prove that the false theta of $frak{sl}_3$, appearing in the character of the vertex algebra $W^0(p)_{A_2}$, can be written as the sum of two depth two quantum modular forms of positive integral weight.