Quantum invariant for torus link and modular forms

被引：24
|
作者：
Hikami, K [1 ]
机构：
[1] Univ Tokyo, Dept Phys, Grad Sch Sci, Tokyo 1130033, Japan
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2004年 / 246卷 / 02期
关键词：
D O I：
10.1007/s00220-004-1046-2
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We consider an asymptotic expansion of Kashaev's invariant or of the colored Jones function for the torus link T(2,2m). We shall give q-series identity related to these invariants, and show that the invariant is regarded as a limit of q being N-th root of unity of the Eichler integral of a modular form of weight 3/2 which is related to the (su) over cap (2)(m-2) character.
引用
收藏
页码：403 / 426
页数：24
相关论文
共 50 条
  • [1] Quantum Invariant for Torus Link and Modular Forms
    Kazuhiro Hikami
    [J]. Communications in Mathematical Physics, 2004, 246 : 403 - 426
  • [2] Torus knots and quantum modular forms
    Hikami, Kazuhiro
    Lovejoy, Jeremy
    [J]. RESEARCH IN THE MATHEMATICAL SCIENCES, 2015, 2 (01)
  • [3] Torus knots and quantum modular forms
    Kazuhiro Hikami
    Jeremy Lovejoy
    [J]. Research in the Mathematical Sciences, 2
  • [4] η-INVARIANT AND MODULAR FORMS
    Han, Fei
    Zhang, Weiping
    [J]. QUARTERLY JOURNAL OF MATHEMATICS, 2015, 66 (01): : 133 - 142
  • [5] MOCK MODULAR FORMS AND QUANTUM MODULAR FORMS
    Choi, Dohoon
    Lim, Subong
    Rhoades, Robert C.
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (06) : 2337 - 2349
  • [6] A modular invariant quantum theory from the connection formulation of (2+1)-gravity on the torus
    Peldan, P
    [J]. CLASSICAL AND QUANTUM GRAVITY, 1996, 13 (02) : 221 - 224
  • [7] On the normalisation of the modular forms in modular invariant theories of flavour
    Petcov, S. T.
    [J]. PHYSICS LETTERS B, 2024, 850
  • [8] Modular forms via invariant theory
    Clery, Fabien
    van der Geer, Gerard
    [J]. RESEARCH IN NUMBER THEORY, 2023, 9 (02)
  • [9] Modular forms via invariant theory
    Fabien Cléry
    Gerard van der Geer
    [J]. Research in Number Theory, 2023, 9
  • [10] Modular invariant of quantum tori
    Castano-Bernard, C.
    Gendron, T. M.
    [J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2014, 109 : 1014 - 1049
12345