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Algebraic aspects of holomorphic quantum modular forms

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arxiv 2403.02880 v2 pith:OAP7P6AB submitted 2024-03-05 math.GT hep-th

Ni An , Stavros Garoufalidis , Shana Yunsheng Li This is my paper · ORCID
classification math.GThep-th
keywords algebraicholomorphicobjectsformsmodularpropertiesquantumarise
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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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  1. The Habiro ring of a number field

    math.NT 2024-12 conditional novelty 8.0 of 10

    A Habiro ring of a number field is constructed, with K3-graded modules, and perturbative quantum invariants are shown to be elements of these modules.

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