# A conjecture of Zagier and the value distribution of quantum modular forms

@inproceedings{Aistleitner2021ACO, title={A conjecture of Zagier and the value distribution of quantum modular forms}, author={Christoph Aistleitner and Bence Borda}, year={2021} }

In his influential paper on quantum modular forms, Zagier developed a conjectural framework describing the behavior of certain quantum knot invariants under the action of the modular group on their argument. More precisely, when JK,0 denotes the colored Jones polynomial of a knot K, Zagier’s modularity conjecture describes the asymptotics of the quotient JK,0(e )/JK,0(e ) as x→ ∞ along rationals with bounded denominators, where γ ∈ SL(2,Z). This problem is most accessible for the figure-eight…

## One Citation

On the order of magnitude of Sudler products

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Given an irrational number $\alpha\in(0,1)$, the Sudler product is defined by $P_N(\alpha) = \prod_{r=1}^{N}2|\sin\pi r\alpha|$. Answering a question of Grepstad, Kaltenbock and Neumuller we prove an…

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