"Examples of mock modular forms"의 두 판 사이의 차이
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imported>Pythagoras0 |
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* mock theta function is essentially a holomorphic part of [[mock modular forms|Mock modular forms]] of weight 1/2 | * mock theta function is essentially a holomorphic part of [[mock modular forms|Mock modular forms]] of weight 1/2 | ||
| + | * Ramanujan found 22 examples | ||
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| − | ==mock theta conjectures | + | ==mock theta conjectures== |
| − | + | * Hickerson1988 http://worldcat.org/issn/0020-9910 | |
| − | * [[ | + | * [[Rank of partition and mock theta conjecture]] |
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==order 3== | ==order 3== | ||
| − | * [[3rd order mock theta functions]] | + | * [[3rd order mock theta functions]] |
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| − | == | + | ==related items== |
| − | + | * [[mock modular forms]] | |
| − | * [[mock | ||
* [[asymptotic analysis of basic hypergeometric series]] | * [[asymptotic analysis of basic hypergeometric series]] | ||
| − | + | ==books== | |
| − | + | * Ramanujan's Lost Notebook: Part I | |
| − | == | + | * Ramanujan's Lost Notebook: Part II |
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| − | + | ==encyclopedia== | |
| + | * http://en.wikipedia.org/wiki/Mock_modular_form | ||
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[[분류:개인노트]] | [[분류:개인노트]] | ||
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[[분류:math and physics]] | [[분류:math and physics]] | ||
[[분류:mock modular forms]] | [[분류:mock modular forms]] | ||
[[분류:math]] | [[분류:math]] | ||
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