Asymptotics and sign patterns for coefficients in expansions of Habiro elements
Number Theory
2024-07-22 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.2204.02628,
title = {Asymptotics and sign patterns for coefficients in expansions of Habiro elements},
author = {Ankush Goswami and Abhash Kumar Jha and Byungchan Kim and Robert Osburn},
journal= {arXiv preprint arXiv:2204.02628},
year = {2024}
}
Comments
17 pages, to appear in Mathematische Zeitschrift