"Examples of mock modular forms"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
(피타고라스님이 이 페이지의 위치를 <a href="/pages/1911026">modular forms</a>페이지로 이동하였습니다.) |
|||
| 20번째 줄: | 20번째 줄: | ||
** George E. Andrews and F. G. Garvan | ** George E. Andrews and F. G. Garvan | ||
* <cite class="" id="CITEREFHickerson1988" style="font-style: normal;">Hickerson, Dean (1988), "A proof of the mock theta conjectures", <em style="">[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''94''' (3): 639–660, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2FBF01394279 10.1007/BF01394279], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=969247 969247], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite><cite class="" id="CITEREFHickerson1988" style="font-style: normal;"><br>[http://worldcat.org/issn/0020-9910 ]</cite> | * <cite class="" id="CITEREFHickerson1988" style="font-style: normal;">Hickerson, Dean (1988), "A proof of the mock theta conjectures", <em style="">[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''94''' (3): 639–660, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2FBF01394279 10.1007/BF01394279], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=969247 969247], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite><cite class="" id="CITEREFHickerson1988" style="font-style: normal;"><br>[http://worldcat.org/issn/0020-9910 ]</cite> | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | |||
| + | <h5>Andrews-Dragonette conjecture</h5> | ||
| + | |||
| + | |||
| 68번째 줄: | 76번째 줄: | ||
[http://mathsci.ucd.ie/%7Ezwegers/papers/006.pdf http://mathsci.ucd.ie/~zwegers/papers/006.pdf] | [http://mathsci.ucd.ie/%7Ezwegers/papers/006.pdf http://mathsci.ucd.ie/~zwegers/papers/006.pdf] | ||
| + | |||
| + | |||
| + | |||
| + | |||
| + | |||
| + | |||
<h5>간단한 소개</h5> | <h5>간단한 소개</h5> | ||
2009년 12월 24일 (목) 14:18 판
Examples
classify which examples are of which use
mock theta function
- mock theta function is essentially a mock modular form of weight 1/2
mock theta conjectures
- Watson, G. N. (1936), "The Final Problem : An Account of the Mock Theta Functions", J. London Math. Soc.11: 55–80, doi:10.1112/jlms/s1-11.1.55
- Watson, G. N. (1937), "The Mock Theta Functions (2)", Proc. London Math. Soc.s2-42: 274–304, doi:10.1112/plms/s2-42.1.274
- Ramanujan's “Lost” Notebook VI: The mock theta conjectures
- George E. Andrews and F. G. Garvan
- Hickerson, Dean (1988), "A proof of the mock theta conjectures", Inventiones Mathematicae94 (3): 639–660, doi:10.1007/BF01394279, MR969247, ISSN0020-9910
[1]
Andrews-Dragonette conjecture
order 3
- \(f(q) = \sum_{n\ge 0} {q^{n^2}\over (-q;q)_n^2} = {2\over \prod_{n>0}(1-q^n)}\sum_{n\in Z}{(-1)^nq^{3n^2/2+n/2}\over 1+q^n}\)
- good introduction is given in Andrews article
- 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 (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.
- The Final Problem : An Account of the Mock Theta Functions
- Watson, G. N. (1936)
- J. London Math. Soc. 11: 55–80
- Some asymptotic formulae for the mock theta series of Ramanujan
- Dragonette, Leila A. (1952),
- Transactions of the American Mathematical Society 72: 474–500
- On the theorems of Watson and Dragonette for Ramanujan's mock theta functions
- Andrews, George E. (1966)
- American Journal of Mathematics 88: 454–490
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 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 (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, http://www.jstor.org/stable/2693766
- Choi, Youn-Seo (2007), "Tenth order mock theta functions in Ramanujan's lost notebook. III", Proceedings of the London Mathematical Society. Third Series94 (1): 26–52, doi:10.1112/plms/pdl006, MR2293464, ISSN0024-6115
http://mathsci.ucd.ie/~zwegers/papers/006.pdf
간단한 소개
하위주제들
하위페이지
재미있는 사실
관련된 단원
많이 나오는 질문
관련된 고교수학 또는 대학수학
관련된 다른 주제들
표준적인 도서 및 추천도서
- Ramanujan's Lost Notebook: Part I
- Ramanujan's Lost Notebook: Part II
- 찾아볼 수학책
- http://gigapedia.info/1/Polyogarithms
- http://gigapedia.info/1/ramanujan
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
참고할만한 자료
- http://www.zentralblatt-math.org/zmath/en/
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Mock_modular_form
- http://viswiki.com/en/
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- 다음백과사전 http://enc.daum.net/dic100/search.do?q=
이미지 검색
동영상
관련기사
네이버 뉴스 검색 (키워드 수정)
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
블로그
- 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
- 트렌비 블로그 검색 http://www.trenb.com/search.qst?q=