### 抄録

Every closed orientable 3-manifold can be constructed by surgery on a link in S^{3}. In the case of surgery along a torus knot, one obtains a Seifert fibered manifold. In this paper we consider three families of such manifolds and study their unified Witten- Reshetikhin-Turaev (WRT) invariants. Thanks to recent computation of the coefficients in the cyclotomic expansion of the colored Jones polynomial for (2, 2t + 1)-torus knots, these WRT invariants can be neatly expressed as q-hypergeometric series which converge inside the unit disk. Using the Rosso-Jones formula and some rather non-standard techniques for Bailey pairs, we find Hecke-type formulas for these invariants. We also comment on their mock and quantum modularity.

元の言語 | 英語 |
---|---|

ページ（範囲） | 249-272 |

ページ数 | 24 |

ジャーナル | Communications in Number Theory and Physics |

巻 | 11 |

発行部数 | 2 |

DOI | |

出版物ステータス | 出版済み - 1 1 2017 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Mathematical Physics
- Physics and Astronomy(all)

### これを引用

*Communications in Number Theory and Physics*,

*11*(2), 249-272. https://doi.org/10.4310/CNTP.2017.v11.n2.a1

**Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants.** / Hikami, Kazuhiro; Lovejoy, Jeremy.

研究成果: ジャーナルへの寄稿 › 記事

*Communications in Number Theory and Physics*, 巻. 11, 番号 2, pp. 249-272. https://doi.org/10.4310/CNTP.2017.v11.n2.a1

}

TY - JOUR

T1 - Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants

AU - Hikami, Kazuhiro

AU - Lovejoy, Jeremy

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Every closed orientable 3-manifold can be constructed by surgery on a link in S3. In the case of surgery along a torus knot, one obtains a Seifert fibered manifold. In this paper we consider three families of such manifolds and study their unified Witten- Reshetikhin-Turaev (WRT) invariants. Thanks to recent computation of the coefficients in the cyclotomic expansion of the colored Jones polynomial for (2, 2t + 1)-torus knots, these WRT invariants can be neatly expressed as q-hypergeometric series which converge inside the unit disk. Using the Rosso-Jones formula and some rather non-standard techniques for Bailey pairs, we find Hecke-type formulas for these invariants. We also comment on their mock and quantum modularity.

AB - Every closed orientable 3-manifold can be constructed by surgery on a link in S3. In the case of surgery along a torus knot, one obtains a Seifert fibered manifold. In this paper we consider three families of such manifolds and study their unified Witten- Reshetikhin-Turaev (WRT) invariants. Thanks to recent computation of the coefficients in the cyclotomic expansion of the colored Jones polynomial for (2, 2t + 1)-torus knots, these WRT invariants can be neatly expressed as q-hypergeometric series which converge inside the unit disk. Using the Rosso-Jones formula and some rather non-standard techniques for Bailey pairs, we find Hecke-type formulas for these invariants. We also comment on their mock and quantum modularity.

UR - http://www.scopus.com/inward/record.url?scp=85027499575&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027499575&partnerID=8YFLogxK

U2 - 10.4310/CNTP.2017.v11.n2.a1

DO - 10.4310/CNTP.2017.v11.n2.a1

M3 - Article

VL - 11

SP - 249

EP - 272

JO - Communications in Number Theory and Physics

JF - Communications in Number Theory and Physics

SN - 1931-4523

IS - 2

ER -