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Journal Article

#### Higher depth quantum modular forms, multiple Eichler integrals, and
sl_{3} false theta functions

##### External Resource

https://doi.org/10.1007/s40687-019-0182-4

(Publisher version)

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##### Fulltext (public)

arXiv:1704.06891.pdf

(Preprint), 376KB

##### Supplementary Material (public)

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##### Citation

Bringmann, K., Kaszian, J., & Milas, A. (2019). Higher depth quantum modular forms,
multiple Eichler integrals, and sl_{3} false theta functions.* Research in the Mathematical
Sciences,* *6*(2): 20. doi:10.1007/s40687-019-0182-4.

Cite as: https://hdl.handle.net/21.11116/0000-0004-7573-7

##### 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 functions of $\mathfrak {sl}_3$, 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.