Asymptotics and sign patterns for coefficients in expansions of Habiro elements

Ankush Goswami; Abhash Kumar Jha; Byungchan Kim; Robert Osburn

doi:10.1007/s00209-023-03307-5

Asymptotics and sign patterns for coefficients in expansions of Habiro elements

Ankush Goswami, Abhash Kumar Jha, Byungchan Kim, Robert Osburn

School of Natural Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	57
Journal	Mathematische Zeitschrift
Volume	304
Issue number	4
DOIs	https://doi.org/10.1007/s00209-023-03307-5
State	Published - Aug 2023

Keywords

Asymptotics
Generalized Fishburn numbers
Habiro ring
Strange identities

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10.1007/s00209-023-03307-5

Cite this

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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{\textquoteright}s result on asymptotics for the Fishburn numbers.",

keywords = "Asymptotics, Generalized Fishburn numbers, Habiro ring, Strange identities",

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N2 - 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.

AB - 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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KW - Strange identities

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Asymptotics and sign patterns for coefficients in expansions of Habiro elements

Abstract

Keywords

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