"Examples of mock modular forms"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
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| 1번째 줄: | 1번째 줄: | ||
| − | ==mock theta function | + | ==mock theta function== |
* 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 | ||
| 11번째 줄: | 11번째 줄: | ||
| − | ==mock theta conjectures<cite class="" id="CITEREFHickerson1988" style="font-style: normal;">[http://worldcat.org/issn/0020-9910 ]</cite> | + | ==mock theta conjectures<cite class="" id="CITEREFHickerson1988" style="font-style: normal;">[http://worldcat.org/issn/0020-9910 ]</cite>== |
* [[5295075|mock theta conjectures]] | * [[5295075|mock theta conjectures]] | ||
| 19번째 줄: | 19번째 줄: | ||
| − | ==Andrews-Dragonette conjecture | + | ==Andrews-Dragonette conjecture== |
* [[rank of partition and mock theta conjecture|rank of partition and mock theta function]] | * [[rank of partition and mock theta conjecture|rank of partition and mock theta function]] | ||
| 27번째 줄: | 27번째 줄: | ||
| − | ==examples | + | ==examples== |
* classify which examples are of which use | * classify which examples are of which use | ||
| 35번째 줄: | 35번째 줄: | ||
| − | ==order 3 | + | ==order 3== |
* [[3rd order mock theta functions]]<br> | * [[3rd order mock theta functions]]<br> | ||
| 43번째 줄: | 43번째 줄: | ||
| − | ==order 5 | + | ==order 5== |
* G.E. Andrews, The fifth and seventh order mock theta functions. Trans. Amer. Math. Soc. 293 (1986), pp. 113–134 | * G.E. Andrews, The fifth and seventh order mock theta functions. Trans. Amer. Math. Soc. 293 (1986), pp. 113–134 | ||
| 52번째 줄: | 52번째 줄: | ||
| − | ==order 7 | + | ==order 7== |
* <cite class="" id="CITEREFHickerson1988" style="font-style: normal;">Hickerson, Dean (1988), "On the seventh order mock theta functions", <em style="">[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''94''' (3): 661–677, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2FBF01394280 10.1007/BF01394280], [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;">Hickerson, Dean (1988), "On the seventh order mock theta functions", <em style="">[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''94''' (3): 661–677, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2FBF01394280 10.1007/BF01394280], [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> | ||
| 60번째 줄: | 60번째 줄: | ||
| − | ==order 8 | + | ==order 8== |
* [[8th order Mock theta functions]] | * [[8th order Mock theta functions]] | ||
| 68번째 줄: | 68번째 줄: | ||
| − | ==order 10 | + | ==order 10== |
* <cite class="" id="CITEREFChoi1999" style="font-style: normal;">Choi, Youn-Seo (1999), "Tenth order mock theta functions in Ramanujan's lost notebook", <em style="">[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''136''' (3): 497–569, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2Fs002220050318 10.1007/s002220050318], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=1695205 1695205], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite> | * <cite class="" id="CITEREFChoi1999" style="font-style: normal;">Choi, Youn-Seo (1999), "Tenth order mock theta functions in Ramanujan's lost notebook", <em style="">[http://en.wikipedia.org/wiki/Inventiones_Mathematicae Inventiones Mathematicae]</em>'''136''' (3): 497–569, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1007%2Fs002220050318 10.1007/s002220050318], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=1695205 1695205], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0020-9910 0020-9910]</cite> | ||
| 80번째 줄: | 80번째 줄: | ||
| − | ==관련된 다른 주제들 | + | ==관련된 다른 주제들== |
* [[mock modular forms|Mock modular forms]] | * [[mock modular forms|Mock modular forms]] | ||
| 89번째 줄: | 89번째 줄: | ||
| − | ==표준적인 도서 및 추천도서 | + | ==표준적인 도서 및 추천도서== |
* [http://gigapedia.com/items:links?id=38285 Ramanujan's Lost Notebook: Part I] | * [http://gigapedia.com/items:links?id=38285 Ramanujan's Lost Notebook: Part I] | ||
| 105번째 줄: | 105번째 줄: | ||
| − | ==참고할만한 자료 | + | ==참고할만한 자료== |
* http://www.zentralblatt-math.org/zmath/en/ | * http://www.zentralblatt-math.org/zmath/en/ | ||
2012년 10월 28일 (일) 15:27 판
mock theta function
- mock theta function is essentially a holomorphic part of Mock modular forms of weight 1/2
- Ramanujan 22 examples
mock theta conjectures[1]
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
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=