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arXiv · 2204.02628

Asymptotics and sign patterns for coefficients in expansions of Habiro elements

Ankush Goswami·Abhash Kumar Jha·Byungchan Kim·Robert Osburn
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Abstract

We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics and discuss positivity for the generalized Fishburn numbers which arise from the Kontsevich-Zagier series associated to the colored Jones polynomial for a family of torus knots. This extends Zagier's result on asymptotics for the Fishburn numbers.

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Ankush Goswami, Abhash Kumar Jha, Byungchan Kim, Robert Osburn. 2023-06-06. Asymptotics and sign patterns for coefficients in expansions of Habiro elements. https://doi.org/10.1007/s00209-023-03307-5

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