### Abstract

The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;ℂ) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2 π √-1. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alexander polynomial evaluated at exp c. In this paper we study cases where it grows polynomially.

Original language | English |
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Pages (from-to) | 815-834 |

Number of pages | 20 |

Journal | Communications in Contemporary Mathematics |

Volume | 10 |

Issue number | SUPPL. 1 |

DOIs | |

Publication status | Published - Nov 1 2008 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications in Contemporary Mathematics*,

*10*(SUPPL. 1), 815-834. https://doi.org/10.1142/S0219199708003034

**Colored Jones polynomials with polynomial growth.** / Hikami, Kazuhiro; Murakami, Hitoshi.

Research output: Contribution to journal › Article

*Communications in Contemporary Mathematics*, vol. 10, no. SUPPL. 1, pp. 815-834. https://doi.org/10.1142/S0219199708003034

}

TY - JOUR

T1 - Colored Jones polynomials with polynomial growth

AU - Hikami, Kazuhiro

AU - Murakami, Hitoshi

PY - 2008/11/1

Y1 - 2008/11/1

N2 - The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;ℂ) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2 π √-1. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alexander polynomial evaluated at exp c. In this paper we study cases where it grows polynomially.

AB - The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;ℂ) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2 π √-1. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alexander polynomial evaluated at exp c. In this paper we study cases where it grows polynomially.

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UR - http://www.scopus.com/inward/citedby.url?scp=56749132480&partnerID=8YFLogxK

U2 - 10.1142/S0219199708003034

DO - 10.1142/S0219199708003034

M3 - Article

VL - 10

SP - 815

EP - 834

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

SN - 0219-1997

IS - SUPPL. 1

ER -