Examples of mock modular forms
imported>Pythagoras0님의 2013년 3월 17일 (일) 15:46 판
mock theta function
- mock theta function is essentially a holomorphic part of Mock modular forms of weight 1/2
- Ramanujan found 22 examples
mock theta conjectures
Andrews-Dragonette conjecture
examples
- classify which examples are of which use
order 3
order 5
- G.E. Andrews, The fifth and seventh order mock theta functions. Trans. Amer. Math. Soc. 293 (1986), pp. 113–134
- Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", Ramanujan revisited (Urbana-Champaign, Ill., 1987),
- Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions
- Basil Gordon and Richard J. Mcintosh
order 7
- Hickerson, Dean (1988), "On the seventh order mock theta functions", Inventiones Mathematicae94 (3): 661–677, doi:10.1007/BF01394280, MR969247, ISSN0020-9910
order 8
order 10
- Choi, Youn-Seo (1999), "Tenth order mock theta functions in Ramanujan's lost notebook", Inventiones Mathematicae136 (3): 497–569, doi:10.1007/s002220050318, MR1695205, ISSN0020-9910
- Choi, Youn-Seo (2000), "Tenth order mock theta functions in Ramanujan's lost notebook. II", Advances in Mathematics156 (2): 180–285, doi:10.1006/aima.2000.1948, MR1808245, ISSN0001-8708
- Choi, Youn-Seo (2007), "Tenth order mock theta functions in Ramanujan's lost notebook. III", Proceedings of the London Mathematical Society. Third Series 94 (1): 26–52, doi:10.1112/plms/pdl006, MR2293464, ISSN 0024-6115
- Choi, Youn-Seo (2002), "Tenth order mock theta functions in Ramanujan's lost notebook. IV", Transactions of the American Mathematical Society354 (2): 705–733, doi:10.1090/S0002-9947-01-02861-6, MR1862564, ISSN0002-9947,
- Zwegers' new proof http://mathsci.ucd.ie/~zwegers/papers/006.pdf
books
- Ramanujan's Lost Notebook: Part I
- Ramanujan's Lost Notebook: Part II