"Examples of mock modular forms"의 두 판 사이의 차이

2010년 7월 31일 (토) 13:56 판

mock theta function

mock theta function is essentially a holomorphic part of Mock modular forms of weight 1/2

mock theta conjectures[1]

mock theta conjectures

Andrews-Dragonette conjecture

rank of partition and mock theta function

examples

classify which examples are of which use

order 3

3rd order mock theta functions

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, MR 969247, ISSN 0020-9910

order 8

8th order Mock theta functions

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, MR 1695205, ISSN 0020-9910
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, MR 1808245, ISSN 0001-8708
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, MR 2293464, 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, MR 1862564, ISSN 0002-9947,
Zwegers' new proof http://mathsci.ucd.ie/~zwegers/papers/006.pdf

@@ 17번째 줄: / 17번째 줄: @@
 <h5>Andrews-Dragonette conjecture</h5>
-* [[rank of partition and mock theta conjecture|Andews and Dragonette]]
+* [[rank of partition and mock theta conjecture|rank of partition and mock theta function]]
@@ 33번째 줄: / 33번째 줄: @@
 <h5>order 3</h5>
-* <math>f(q) = \sum_{n\ge 0} {q^{n^2}\over (-q;q)_n^2}  = {2\over \prod_{n>0}(1-q^n)}\sum_{n\in Z}{(-1)^nq^{3n^2/2+n/2}\over 1+q^n}</math><br>[http://www.research.att.com/%7Enjas/sequences/A000025 ][http://www.research.att.com/%7Enjas/sequences/A000025 http://www.research.att.com/~njas/sequences/A000025]<br>[http://www.research.att.com/%7Enjas/sequences/b000025.txt http://www.research.att.com/~njas/sequences/b000025.txt]<br>
+* [[3rd order mock theta functions]]<br>
-*  good introduction is given in Andrews article <br>
-** [http://www.ingentaconnect.com/content/klu/rama/2003/00000007/F0030001/05142410 Partitions : at the interface of q-series and modular forms]
-** [http://www.ingentaconnect.com/content/klu/rama/2003/00000007/F0030001/05142410 ]section 5
-* the asymptotic series for coefficients of the order 3 mock theta function f(q) studied by of (Andrews 1966) and Dragonette (1952) converges to the coefficients ([http://www.springerlink.com/content/5524655155350464/ Bringmann & Ono 2006]).
-* In particular Mock theta functions have asymptotic expansions at cusps of the modular group, acting on the upper half-plane, that resemble those of modular forms of weight 1/2 with poles at the cusps.
-* [http://dx.doi.org/10.1112%2Fjlms%2Fs1-11.1.55 The Final Problem : An Account of the Mock Theta Functions]<br>
-** Watson, G. N. (1936),  J. London Math. Soc. 11: 55–80
-* [http://dx.doi.org/10.2307%2F1990714 Some asymptotic formulae for the mock theta series of Ramanujan]<br>
-** Dragonette, Leila A. (1952),
-** Transactions of the American Mathematical Society 72: 474–500
-* [http://dx.doi.org/10.2307%2F2373202 On the theorems of Watson and Dragonette for Ramanujan's mock theta functions]<br>
-** Andrews, George E. (1966)
-** American Journal of Mathematics 88: 454–490
@@ 69번째 줄: / 58번째 줄: @@
 <h5>order 8</h5>
-* [[#]]
+* [[8th order Mock theta functions]]

"Examples of mock modular forms"의 두 판 사이의 차이

2010년 7월 31일 (토) 13:56 판

목차

mock theta function

mock theta conjectures[1]

Andrews-Dragonette conjecture

examples

order 3

order 5

order 7

order 8

order 10

관련된 다른 주제들

표준적인 도서 및 추천도서

참고할만한 자료

둘러보기 메뉴

검색