Ramanujan's Mock Theta Functions and Their Applications [d'après Zwegers and Ono-Bringmann]
Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Exposé no. 986, 22 p.
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Zagier, Don. Ramanujan's Mock Theta Functions and Their Applications [d'après Zwegers and Ono-Bringmann], dans Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Exposé no. 986, 22 p. http://www.numdam.org/item/AST_2009__326__143_0/

[1] G. E. Andrews - "The fifth and seventh order mock theta functions", Trans. Amer. Math. Soc. 293 (1986), p. 113-134. | DOI | MR | Zbl

[2] G. E. Andrews - "Ramanujan's fifth order mock theta functions as constant terms", in Ramanujan revisited (Urbana-Champaign, Ill., 1987), Academic Press, 1988, p. 47- 56. | MR | Zbl

[3] M. P. Appell - "Sur les fonctions doublement périodiques de troisième espèce I", Annales sci. de l'ENS 1 (1884), p. 135, | EuDML | JFM | Numdam | MR

M. P. Appell - "Sur les fonctions doublement périodiques de troisième espèce I", Annales sci. de l'ENS 2 (1885), p. 9, and | JFM | Numdam | MR

M. P. Appell - "Sur les fonctions doublement périodiques de troisième espèce I", Annales sci. de l'ENS 3 (1886), p. 9. | EuDML | JFM | Numdam | MR

[4] A. O. L. Atkin & P. Swinnerton-Dyer - "Some properties of partitions", Proc. London Math. Soc. 4 (1954), p. 84-106. | DOI | MR | Zbl

[5] K. Bringmann - "Asymptotics for rank partition functions", Trans. Amer. Math. Soc. 361 (2009), p. 3483-3500. | DOI | MR | Zbl

[6] K. Bringmann & K. Ono - "The f ( q ) mock theta function conjecture and partition ranks", Invent. Math. 165 (2006), p. 243-266. | DOI | MR | Zbl

[7] K. Bringmann & K. Ono - "Dyson's ranks and Maass forms", to appear in Ann. Math. | MR | Zbl

[8] F. J. Dyson - "Some guesses in the theory of partitions", Eureka 8 (1944), p. 10-15. | MR

[9] M. Eichler & D. Zagier - The theory of Jacobi forms, Progress in Math., vol. 55, Birkhäuser, 1985. | MR | Zbl

[10] L. Göttsche & D. Zagier - "Jacobi forms and the structure of Donaldson invariants for 4 -manifolds with b + = 1 ", Selecta Math. (N.S.) 4 (1998), p. 69 - 115. | DOI | MR | Zbl

[11] D. Hickerson - "A proof of the mock theta conjectures", Invent. Math. 94 (1988), p. 639-660. | DOI | EuDML | MR | Zbl

[12] D. Hickerson - "On the seventh order mock theta functions", Invent. Math. 94 (1988), p. 661-677. | DOI | EuDML | MR | Zbl

[13] M. Kaneko & D. Zagier - "A generalized Jacobi theta function and quasimodular forms", in The moduli space of curves (Texel Island, 1994), Progr. Math., vol. 129, Birkhäuser, 1995, p. 165-172. | DOI | MR | Zbl

[14] R. Lawrence & D. Zagier - "Modular forms and quantum invariants of 3-manifolds", Asian J. Math. 3 (1999), p. 93-107. | DOI | MR | Zbl

[15] M. Lerch - "Bemerkungen zur Theorie der elliptischen Funktionen", Jahrbuch über die Fortschritte der Mathematik 24 (1892), p. 442-445. | JFM

[16] M. Lerch - "Poznámky k theorii funkcÍ elliptických", Rozpravy České Akademie CÍsaře Frantiska Josefa pro vědy, slovesnost a uměnÍ v praze 24 (1892), p. 465-480.

[17] L. J. Mordell - "The value of the definite integral - e a t 2 + b t e c t + d d t , Quarterly J. of Math. 68 (1920), p. 329-342. | JFM

[18] W. Nahm - "Conformal field theory and torsion elements of the Bloch group", in Frontiers in number theory, physics, and geometry II, Springer, 2007, p. 67-132. | DOI | MR | Zbl

[19] A. Polishchuk - "M. P. Appell's function and vector bundles of rank 2 on elliptic curves", Ramanujan J. 5 (2001), p. 111-128. | DOI | Zbl

[20] S. Ramanujan - The lost notebook and other unpublished papers, Narosa Publishing House, New Delhi, 1987. | Zbl

[21] A. M. Semikhatov, A. Taormina & I. Y. Tipunin - "Higher-level Appell functions, modular transformations, and characters", Comm. Math. Phys. 255 (2005), p. 469-512. | DOI | Zbl

[22] A. Sen - "Walls of marginal stability and dyon spectrum in 𝒩 = 4 supersymmetric string theories", J. High Energy Phys. 5 (2007).

[23] G. N. Watson - "The final problem: an account of the mock theta functions", J. Lond. Math. Soc. 11 (1936), p. 55-80. | DOI | JFM | Zbl

[24] D. Zagier - "Nombres de classes et formes modulaires de poids 3/2", C. R. Acad. Sci. Paris Sér. A-B 281 (1975), p. A883-A886. | Zbl

[25] D. Zagier - "The dilogarithm function", in Frontiers in number theory, physics, and geometry II, Springer, 2007, p. 3-65. | DOI | Zbl

[26] D. Zagier - "Elliptic modular forms and their applications", in The 1-2-3 of modular forms, Universitext, Springer, 2008, p. 1-103. | Zbl

[27] S. P. Zwegers - "Mock θ-functions and real analytic modular forms", in q-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), Contemp. Math., vol. 291, Amer. Math. Soc., 2001, p. 269-277. | DOI | Zbl

[28] S. P. Zwegers - "Mock theta functions", Ph.D. Thesis, Universiteit Utrecht, 2002, http://igitur-archive.library.uu.nl/dissertations/2003-0127-094324/full.pdf. | Zbl