[1] Andersen, J. E. and Hansen, S. K. Asymptotics of the quantum invariants for surgeries on the figure 8 knot. J. Knot Theory Ramifications 15 (2006), 479–548.

[2] Dimofte, T. D. and Garoufalidis, S. The quantum content of the gluing equations. Geom. Topol. 17 (2013), 1253–1315.

[3] Dimofte, T., Gukov, S., Lenells, J. and Zagier, D. Exact results for perturbative Chern–Simons theory with complex gauge group. Commun. Number Theory Phys. 3 (2009), 363–443.

[4] Dubois, J. and Kashaev, R. On the asymptotic expansion of the colored Jones polynomial for torus knots. Math. Ann. 339 (2007), 757–782.

[5] Faddeev, L. D. Discrete Heisenberg–Weyl group and modular group. Lett. Math. Phys. 34 (1995), 249–254.

[6] Faddeev, L. D. and Kashaev, R. M. Strongly coupled quantum discrete Liouville theory. II. Geometric interpretation of the evolution operator. J. Phys. A 35 (2002), 4043–4048.

[7] Faddeev, L. D., Kashaev, R. M. and Yu, A. Volkov. Strongly coupled quantum discrete Liouville theory. I. Algebraic approach and duality. Comm. Math. Phys. 219 (2001), 199–219.

[8] Garoufalidis, S. and Le, T. T. Q. On the volume conjecture for small angles. arXiv:math/0502163.

[9] Gukov, S. Three-dimensional quantum gravity, Chern–Simons theory, and the A-polynomial. Comm. Math. Phys. 255 (2005), 577–627.

[10] Gukov, S. and Murakami, H. SL(2, ℂ) Chern–Simons theory and the asymptotic behavior of the colored Jones polynomial. Lett. Math. Phys. 86 (2008), 79–98.

[11] Hikami, K. Quantum invariant for torus link and modular forms. Comm. Math. Phys. 246 (2004), 403–426.

[12] Kashaev, R. M. Quantum dilogarithm as a 6j-symbol. Modern Phys. Lett. A9 (1994), 3757–3768.

[13] Kashaev, R. M. A link invariant from quantum dilogarithm. Mod. Phys. Lett. A10 (1995), 1409–1418.

[14] Kashaev, R. M. The hyperbolic volume of knots from the quantum dilogarithm. Lett. Math. Phys. 39 (1997), 269–275.

[15] Kashaev, R. M. and Tirkkonen, O. A proof of the volume conjecture on torus knots (Russian). Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 269 (2000), *Vopr. Kvant. Teor. Polya i Stat. Fiz.* **16**, 262–268, 370; translation in *J. Math. Sci.* (N.Y.) **115** (2003), 2033–2036.

[16] Kashaev, R. M. and Yokota, Y. On the volume conjecture for the knot 5_{2}. preprint.

[17] Murakami, H. An introduction to the volume conjecture. Interactions between hyperbolic geometry, quantum topology and number theory, *Contemp. Math.* 541 (Amer. Math. Soc., Providence, RI, 2011), 1–40.

[18] Murakami, H. and Murakami, J. The coloured Jones polynomials and the simplicial volume of a knot. Acta Math. 186 (2001), 85–104.

[19] Murakami, H., Murakami, J., Okamoto, M., Takata, T. and Yokota, Y. Kashaev's conjecture and the Chern–Simons invariants of knots and links. Experiment. Math. 11 (2002), 427–435.

[20] Ohtsuki, T. On the asymptotic expansion of the Kashaev invariant of the 5_{2} knot. Quantum Topology 7 (2016), 669–735.

[21] Ohtsuki, T. On the asymptotic expansion of the Kashaev invariant of the hyperbolic knots with 7 crossings. preprint.

[22] Ohtsuki, T. and Takata, T. On the Kashaev invariant and the twisted Reidemeister torsion of two-bridge knots. Geom. Topol. 19 (2015), 853–952.

[23] Stein, E. M. and Weiss, G. Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series 32 (Princeton University Press, Princeton, N.J., 1971).

[24] Takata, T. On the asymptotic expansions of the Kashaev invariant of some hyperbolic knots with 8 crossings. preprint.

[25] Thurston, D. P. Hyperbolic volume and the Jones polynomial. Notes accompanying lectures at the summer school on quantum invariants of knots and three-manifolds (Joseph Fourier Institute, University of Grenoble, org. C. Lescop, June, 1999), http://www.math.columbia.edu/~dpt/speaking/Grenoble.pdf. [26] van der Veen, R. Proof of the volume conjecture for Whitehead chains. Acta Math. Vietnam 33 (2008), 421–431.

[27] van der Veen, R. A cabling formula for the coloured Jones polynomial. arXiv:0807.2679.

[28] Yamazaki, M. and Yokota, Y. On the limit of the colored Jones polynomial of a non-simple link. Tokyo J. Math. 33 (2010), 537–551.

[29] Witten, E. Analytic continuation of Chern–Simons theory. Chern–Simons gauge theory: 20 years after. AMS/IP Stud. Adv. Math., 50 (Amer. Math. Soc., Providence, RI, 2011), 347–446.

[30] Wong, R. Asymptotic approximations of integrals. Computer Science and Scientific Computing (Academic Press, Inc., Boston, MA, 1989).

[31] Woronowicz, S. L. Quantum exponential function. Rev. Math. Phys. 12 (2000), 873–920.

[32] Yokota, Y. On the volume conjecture for hyperbolic knots. math.QA/0009165.

[33] Yokota, Y. From the Jones polynomial to the A-polynomial of hyperbolic knots. *Proceedings of the Winter Workshop of Topology/Workshop of Topology and Computer* (Sendai, 2002/Nara, 2001). Interdiscip. Inform. Sci. 9 (2003), 11–21.

[34] Yokota, Y. On the Kashaev invariant of twist knots. “Intelligence of Low-dimensional Topology” (edited by Ohtsuki, T. and Wakui, M.), RIMS Kokyuroku 1766 (2011), 45–51.

[35] Zagier, D. Quantum modular forms. Quanta of maths. Clay Math. Proc. 11 (Amer. Math. Soc., Providence, RI, 2010), 659–675.

[36] Zheng, H. Proof of the volume conjecture for Whitehead doubles of a family of torus knots. Chin. Ann. Math. Ser. B 28 (2007), 375–388.