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

University of Texas Rio Grande Valley
Indian Institute of Technology Banaras Hindu University
University College Dublin

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

2 Scopus citations

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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title = "Asymptotics and sign patterns for coefficients in expansions of Habiro elements",

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",

author = "Ankush Goswami and Jha, \{Abhash Kumar\} and Byungchan Kim and Robert Osburn",

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AU - Kim, Byungchan

AU - Osburn, Robert

PY - 2023/8

Y1 - 2023/8

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.

KW - Asymptotics

KW - Generalized Fishburn numbers

KW - Habiro ring

KW - Strange identities

UR - https://www.scopus.com/pages/publications/85164522443

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DO - 10.1007/s00209-023-03307-5

M3 - Article

AN - SCOPUS:85164522443

SN - 0025-5874

VL - 304

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 4

M1 - 57

ER -

Asymptotics and sign patterns for coefficients in expansions of Habiro elements

Abstract

Keywords

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