참고문헌
- G. E. Andrews , Mordell integrals and Ramanujan's 'lost' notebook, Analytic number theory (Philadelphia, PA., 1980), pp. 10-18, Lecture Notes in Math., 899, Springer, Berlin-New York, 1981.
- G. E. Andrews, R. Rhoades, and S. Zwegers, Modularity of the concave composition generating function, Algebra Number Theory 7 (2013), no. 9, 2103-2139. https://doi.org/10.2140/ant.2013.7.2103
-
M. C. N. Cheng, K3 surfaces, N = 4 Dysons, and the Mathieu group
$M_{24}$ , arxiv:1005.5415 (2010). - M. C. N. Cheng, J. F. R Duncan, and J. A. Harvey, Umbral moonshine, Commun. Number Theory Phys. 8 (2014), no. 2, 101-242. https://doi.org/10.4310/CNTP.2014.v8.n2.a1
- A. Dabholkar, S. Murthy, and D. Zagier, Quantum Black Holes, Wall Crossing, and Mock Modular Forms, arXiv:1208.4074 [hep-th].
- J. F. R. Duncan, M. Griffin, and K. Ono, Proof of the umbral moonshine conjecture, Res. Math. Sci. 2 (2015), Art. 26, 47 pp. https://doi.org/10.1186/s40687-015-0044-7
- T. Eguchi, H. Ooguri, and Y. Tachikawa, Notes on the K3 surface and the Mathieu group M24, Exp. Math. 20 (2011), no. 1, 91-96. https://doi.org/10.1080/10586458.2011.544585
- T. Eguchi, H. Ooguri, S.-K. Yang, and A. Taormina, Superconformal algebra and string compactification on manifolds with SU(N) Holonomy, Nuclear Phys. B 315 (1989), no. 1, 193-221. https://doi.org/10.1016/0550-3213(89)90454-9
- T. Eguchi, Y. Sugawara, and A. Taormina, On the unitary representation of N = 2 and N = 4 superconformal algebras, Phys. Lett. B 210 (1988), no. 1-2, 125-132. https://doi.org/10.1016/0370-2693(88)90360-7
- A. Folsom, S. Garthwaite, S.-Y. Kang, H. Swisher, and S. Treneer, Quantum mock modular forms arising from eta-theta fnctions, Res. Number Theory 2 (2016), Art. 14, 41 pp. https://doi.org/10.1007/s40993-016-0045-7
- B. Gordon and R. J. McIntosh, A survey of classical mock theta functions, Partitions, q-Series, and Modular Forms, pp. 95-144, Springer, Berlin, 2012.
- K. Hikami, Transformation formula of the second order mock theta functions, Lett. Math. Phys. 75 (2006), no. 1, 93-98. https://doi.org/10.1007/s11005-005-0039-1
- S.-Y. Kang, Generalizations of Ramanujan's reciprocity theorem and their applications, J. Lond. Math. Soc. 75 (2007), no. 2, 18-34. https://doi.org/10.1112/jlms/jdl002
- S.-Y. Kang, Mock Jacobi forms in basic hypergeometric series, Compos. Math. 145 (2009), no. 3, 553-565. https://doi.org/10.1112/S0010437X09004060
- R. J. McIntosh, Second order mock theta functions, Canad. Math. Bull. 50 (2007), no. 2, 284-290. https://doi.org/10.4153/CMB-2007-028-9
- K. Ono, Unearthing the visions of a master: harmonic Maass forms and number theory, Current developments in mathematics, 2008, 347-454, Int. Press, Somerville, MA, 2009.
- S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.
- G. N. Watson, The final problem: An account of the mock theta functions, J. London Math. Soc. 11 (1936), 55-80.
- D. Zagier, Ramanujan's mock theta functions and their applications, Seminaire Bourbaki 60eme annee (986) (2006-2007); http://www.bourbaki.ens.fr/TEXTES/986.pdf.
- S. P. Zwegers, Mock Theta Functions and Real Analytic Modular Forms, q-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), Contemp. Math., vol. 291, Amer. Math. Soc., Providence, RI, 2001, pp. 269-277, DOI: 10.1090/conm/291/04907.
- S. P. Zwegers, Mock Theta Functions, Thesis, Utrecht, 2002.
- S. P. Zwegers, Multivariable Appell Functions, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.164.6121.(2010).
- S. P. Zwegers, Appell-Lerch sums, School and Conference on Modular Forms and Mock Modular Forms and their Applications in Arithmetic, Geometry and Physics, 2011. http://indico.ictp.it/event/a10129/session/42/contribution/25/material/0/0.pdf.