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The elliptic genera of the K3 surfaces, both compact and non-compact cases, are studied by using the theory of mock theta functions.
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R. Lawrence and D. Zagier, Modular forms and quantum invariants of 3-manifolds , Asian J. Math. 3
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J. H. Bruinier, Borcherds Products on O ( 2 , ℓ ) O(2,\ell) and Chern Classes of Heegner Divisors , vol. 1780
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S. P. Zwegers, Mock Theta Functions , Ph.D. thesis, Universiteit Utrecht (2002)
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J. H. Bruinier and J. Funke, On two geometric theta lifts , Duke Math. J. 125
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K. Hikami, Quantum invariant for torus link and modular forms , Commun. Math. Phys. 246
2004
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T. Eguchi, Y. Sugawara, and A. Taormina, Liouville field, modular forms and elliptic genera , JHEP 2007
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A. Maloney and E. Witten, Quantum gravity partition function in three dimensions , arXiv:0712.0155
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J. Manschot and G. W. Moore, A modern Farey tail , arXiv:0712.0573
2007
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D. Zagier, Ramanujan’s mock theta functions and their applications [d’après Zwegers and Bringmann–Ono] , Séminaire Bourbaki 986
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———, Unearthing the visions of a master: harmonic Maass forms and number theory , Proceedings of the 2008 Harvard-MIT Current Developments in Mathematics Conference, Intl. Press, Boston, in press
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T. Eguchi and K. Hikami, Superconformal algebras and mock theta functions , J. Phys. A: Math. Theor. 42
2009
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B. Gordon and R. J. McIntosh, A survey of classical mock theta functions , preprint (2009)
2009
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