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Regular and Chaotic Dynamics, 2005, Volume 10, Issue 4, Pages 509–530
DOI: https://doi.org/10.1070/RD2005v010n04ABEH000328
(Mi rcd723)
 

This article is cited in 36 scientific papers (total in 36 papers)

Bicentennial of C.G. Jacobi

Mock (false) theta functions as quantum invariants

K. Hikami

Graduate School of Science, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan
Citations (36)
Abstract: We establish a correspondence between the $\mathrm{SU(2)}$ Witten–Reshetikhin–Turaev invariant for the Seifert manifold $M(p_1,p_2,p_3)$ and Ramanujan's mock theta functions.
Keywords: quantum invariant, modular form, mock theta function, Seifert manifold, q-hypergeometric function.
Received: 20.06.2005
Accepted: 19.09.2005
Bibliographic databases:
Document Type: Article
MSC: 33D15, 57M27, 11F37
Language: English
Citation: K. Hikami, “Mock (false) theta functions as quantum invariants”, Regul. Chaotic Dyn., 10:4 (2005), 509–530
Citation in format AMSBIB
\Bibitem{Hik05}
\by K.~Hikami
\paper Mock (false) theta functions as quantum invariants
\jour Regul. Chaotic Dyn.
\yr 2005
\vol 10
\issue 4
\pages 509--530
\mathnet{http://mi.mathnet.ru/rcd723}
\crossref{https://doi.org/10.1070/RD2005v010n04ABEH000328}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2191375}
\zmath{https://zbmath.org/?q=an:1133.57301}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2005RCD....10..509H}
Linking options:
  • https://www.mathnet.ru/eng/rcd723
  • https://www.mathnet.ru/eng/rcd/v10/i4/p509
  • This publication is cited in the following 36 articles:
    1. Campbell Wheeler, “Quantum Modularity for a Closed Hyperbolic 3-Manifold”, SIGMA, 21 (2025), 004, 74 pp.  mathnet  crossref
    2. Toshiki Matsusaka, Springer Proceedings in Mathematics & Statistics, 456, Low Dimensional Topology and Number Theory, 2025, 133  crossref
    3. Miranda C. N. Cheng, Ioana Coman, Davide Passaro, Gabriele Sgroi, “Quantum Modular $\widehat Z^G$-Invariants”, SIGMA, 20 (2024), 018, 52 pp.  mathnet  crossref
    4. Francesca Ferrari, Pavel Putrov, “Supergroups, q-Series and 3-Manifolds”, Ann. Henri Poincaré, 25:5 (2024), 2781  crossref
    5. Yuya Murakami, “Witten–Reshetikhin–Turaev invariants and indefinite false theta functions for plumbing indefinite H-graphs”, J. Knot Theory Ramifications, 33:12 (2024)  crossref
    6. Kathrin Bringmann, Chris Jennings-Shaffer, Antun Milas, “Graph schemes, graph series, and modularity”, Journal of Combinatorial Theory, Series A, 197 (2023), 105749  crossref
    7. Chuanan Wei, Yuanbo Yu, Qiuxia Hu, “Two generalizations of Jacobi's triple product identity and their applications”, Ramanujan J, 60:4 (2023), 925  crossref
    8. Jørgen Ellegaard Andersen, William Elbæk Mistegård, “Resurgence analysis of quantum invariants of Seifert fibered homology spheres”, Journal of London Math Soc, 105:2 (2022), 709  crossref
    9. Hans Jockers, Peter Mayr, Urmi Ninad, Alexander Tabler, “BPS indices, modularity and perturbations in quantum K-theory”, J. High Energ. Phys., 2022:2 (2022)  crossref
    10. Hu Q., “Some New Representations of Hikami'S Second-Order Mock Theta Function D-5(Q)”, Turk. J. Math., 2021  crossref  mathscinet  isi  scopus
    11. Gukov S., Park S., Putrov P., “Cobordism Invariants From Bps Q-Series”, Ann. Henri Poincare, 22:12 (2021), 4173–4203  crossref  mathscinet  isi  scopus
    12. Cheng M.C.N., Ferrari F., Sgroi G., “Three-Manifold Quantum Invariants and Mock Theta Functions”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 378:2163, SI (2020), 20180439  crossref  mathscinet  zmath  isi  scopus
    13. Cheng M.C.N., Chun S., Ferrari F., Gukov S., Harrison S.M., “3D Modularity”, J. High Energy Phys., 2019, no. 10, 010  crossref  isi  scopus
    14. Kucharski P., “(Z)Over-Cap Invariants At Rational Tau”, J. High Energy Phys., 2019, no. 9, 092  crossref  mathscinet  isi  scopus
    15. Bringmann K., Nazaroglu C., “A Framework For Modular Properties of False Theta Functions”, Res. Math. Sci., 6:3 (2019), 30  crossref  mathscinet  zmath  isi  scopus
    16. Chen B., “Bilateral Series and Ramanujan Radial Limits of Mock (False) Theta Functions”, Int. J. Math., 30:4 (2019), 1950023  crossref  mathscinet  zmath  isi  scopus
    17. Bin Chen, “On the dual nature theory of bilateral series associated to mock theta functions”, Int. J. Number Theory, 14:01 (2018), 63  crossref
    18. Byungchan Kim, Jeremy Lovejoy, “Ramanujan-type partial theta identities and conjugate Bailey pairs, II. Multisums”, Ramanujan J, 46:3 (2018), 743  crossref
    19. George E. Andrews, Bruce C. Berndt, Ramanujan's Lost Notebook, 2018, 365  crossref
    20. Kathrin Bringmann, Amanda Folsom, Antun Milas, “Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters”, Journal of Mathematical Physics, 58:1 (2017)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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