Asymptotics and sign patterns for coefficients in expansions of Habiro elements

Authors

Ankush Goswami, The University of Texas Rio Grande Valley
Abhash Kumar Jha
Byungchan Kim
Robert Osburn

Document Type

Article

Publication Date

7-10-2023

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.

Comments

Copyright © 2023, The Author(s)

Recommended Citation

Goswami, A., Jha, A.K., Kim, B. et al. Asymptotics and sign patterns for coefficients in expansions of Habiro elements. Math. Z. 304, 57 (2023). https://doi.org/10.1007/s00209-023-03307-5

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Mathematische Zeitschrift

DOI

https://doi.org/10.1007/s00209-023-03307-5