Algebraic aspects of holomorphic quantum modular forms

Ni An; Stavros Garoufalidis; Shana Yunsheng Li

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arXiv · 2403.02880

Algebraic aspects of holomorphic quantum modular forms

Ni An·Stavros Garoufalidis·Shana Yunsheng Li

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Abstract

Matrix-valued holomorphic quantum modular forms are intricate objects that arise in successive refinements of the Volume Conjecture of knots and involve three holomorphic, asymptotic and arithmetic objects. It is expected that the algebraic properties of these objects can be deduced from the algebraic properties of descendant state integrals, and we illustrate this for the case of the $(-2,3,7)$-pretzel knot.

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Ni An, Stavros Garoufalidis, Shana Yunsheng Li. 2024-07-12. Algebraic aspects of holomorphic quantum modular forms. https://arxiv.org/abs/2403.02880

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