"Examples of mock modular forms"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 8번째 줄: | 8번째 줄: | ||
==mock theta conjectures== | ==mock theta conjectures== | ||
| + | * conjecture by Andrews-Dragonette | ||
* Hickerson1988 http://worldcat.org/issn/0020-9910 | * Hickerson1988 http://worldcat.org/issn/0020-9910 | ||
* [[Rank of partition and mock theta conjecture]] | * [[Rank of partition and mock theta conjecture]] | ||
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==examples== | ==examples== | ||
| 65번째 줄: | 56번째 줄: | ||
==order 10== | ==order 10== | ||
| − | + | * [[10th order mock theta functions]] | |
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2013년 3월 17일 (일) 16:19 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
- conjecture by Andrews-Dragonette
- Hickerson1988 http://worldcat.org/issn/0020-9910
- Rank of partition and mock theta 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
books
- Ramanujan's Lost Notebook: Part I
- Ramanujan's Lost Notebook: Part II