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arXiv · 1704.06891

Higher depth quantum modular forms, multiple Eichler integrals, and $\frak{sl}_3$ false theta functions

Kathrin Bringmann·Jonas Kaszian·Antun Milas
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Abstract

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.

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Kathrin Bringmann, Jonas Kaszian, Antun Milas. 2017-04-23. Higher depth quantum modular forms, multiple Eichler integrals, and $\frak{sl}_3$ false theta functions. https://arxiv.org/abs/1704.06891

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