@incollection{AST_2009__326__143_0, author = {Zagier, Don}, title = {Ramanujan's {Mock} {Theta} {Functions} and {Their} {Applications} [d'apr\`es {Zwegers} and {Ono-Bringmann]}}, booktitle = {S\'eminaire Bourbaki Volume 2007/2008 Expos\'es 982-996}, series = {Ast\'erisque}, note = {talk:986}, pages = {143--164}, publisher = {Soci\'et\'e math\'ematique de France}, number = {326}, year = {2009}, mrnumber = {2605321}, zbl = {1198.11046}, language = {en}, url = {http://archive.numdam.org/item/AST_2009__326__143_0/} }
TY - CHAP AU - Zagier, Don TI - Ramanujan's Mock Theta Functions and Their Applications [d'après Zwegers and Ono-Bringmann] BT - Séminaire Bourbaki Volume 2007/2008 Exposés 982-996 AU - Collectif T3 - Astérisque N1 - talk:986 PY - 2009 SP - 143 EP - 164 IS - 326 PB - Société mathématique de France UR - http://archive.numdam.org/item/AST_2009__326__143_0/ LA - en ID - AST_2009__326__143_0 ER -
%0 Book Section %A Zagier, Don %T Ramanujan's Mock Theta Functions and Their Applications [d'après Zwegers and Ono-Bringmann] %B Séminaire Bourbaki Volume 2007/2008 Exposés 982-996 %A Collectif %S Astérisque %Z talk:986 %D 2009 %P 143-164 %N 326 %I Société mathématique de France %U http://archive.numdam.org/item/AST_2009__326__143_0/ %G en %F AST_2009__326__143_0
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://archive.numdam.org/item/AST_2009__326__143_0/
[1] The fifth and seventh order mock theta functions", Trans. Amer. Math. Soc. 293 (1986), p. 113-134. | DOI | MR | Zbl
- "[2] 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] Sur les fonctions doublement périodiques de troisième espèce I", Annales sci. de l'ENS 1 (1884), p. 135, | EuDML | JFM | Numdam | MR
- "Sur les fonctions doublement périodiques de troisième espèce I", Annales sci. de l'ENS 2 (1885), p. 9, and | JFM | Numdam | MR
- "Sur les fonctions doublement périodiques de troisième espèce I", Annales sci. de l'ENS 3 (1886), p. 9. | EuDML | JFM | Numdam | MR
- "[4] Some properties of partitions", Proc. London Math. Soc. 4 (1954), p. 84-106. | DOI | MR | Zbl
& - "[5] Asymptotics for rank partition functions", Trans. Amer. Math. Soc. 361 (2009), p. 3483-3500. | DOI | MR | Zbl
- "[6] The mock theta function conjecture and partition ranks", Invent. Math. 165 (2006), p. 243-266. | DOI | MR | Zbl
& - "[7] Dyson's ranks and Maass forms", to appear in Ann. Math. | MR | Zbl
& - "[8] Some guesses in the theory of partitions", Eureka 8 (1944), p. 10-15. | MR
- "[9] The theory of Jacobi forms, Progress in Math., vol. 55, Birkhäuser, 1985. | MR | Zbl
& -[10] Jacobi forms and the structure of Donaldson invariants for -manifolds with ", Selecta Math. (N.S.) 4 (1998), p. 69 - 115. | DOI | MR | Zbl
& - "[11] A proof of the mock theta conjectures", Invent. Math. 94 (1988), p. 639-660. | DOI | EuDML | MR | Zbl
- "[12] On the seventh order mock theta functions", Invent. Math. 94 (1988), p. 661-677. | DOI | EuDML | MR | Zbl
- "[13] 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] Modular forms and quantum invariants of 3-manifolds", Asian J. Math. 3 (1999), p. 93-107. | DOI | MR | Zbl
& - "[15] Bemerkungen zur Theorie der elliptischen Funktionen", Jahrbuch über die Fortschritte der Mathematik 24 (1892), p. 442-445. | JFM
- "[16] Poznámky k theorii funkcÍ elliptických", Rozpravy České Akademie CÍsaře Frantiska Josefa pro vědy, slovesnost a uměnÍ v praze 24 (1892), p. 465-480.
- "[17] The value of the definite integral , Quarterly J. of Math. 68 (1920), p. 329-342. | JFM
- "[18] 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] M. P. Appell's function and vector bundles of rank 2 on elliptic curves", Ramanujan J. 5 (2001), p. 111-128. | DOI | Zbl
- "[20] The lost notebook and other unpublished papers, Narosa Publishing House, New Delhi, 1987. | Zbl
-[21] Higher-level Appell functions, modular transformations, and characters", Comm. Math. Phys. 255 (2005), p. 469-512. | DOI | Zbl
, & - "[22] Walls of marginal stability and dyon spectrum in supersymmetric string theories", J. High Energy Phys. 5 (2007).
- "[23] The final problem: an account of the mock theta functions", J. Lond. Math. Soc. 11 (1936), p. 55-80. | DOI | JFM | Zbl
- "[24] 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] The dilogarithm function", in Frontiers in number theory, physics, and geometry II, Springer, 2007, p. 3-65. | DOI | Zbl
- "[26] Elliptic modular forms and their applications", in The 1-2-3 of modular forms, Universitext, Springer, 2008, p. 1-103. | Zbl
- "[27] 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] Mock theta functions", Ph.D. Thesis, Universiteit Utrecht, 2002, http://igitur-archive.library.uu.nl/dissertations/2003-0127-094324/full.pdf. | Zbl
- "