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

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Examples
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==introduction==
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* mock theta function is essentially a holomorphic part of [[mock modular forms|Mock modular forms]] of weight 1/2
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* Ramanujan found 17 examples
  
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classify which examples are of which use
 
  
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==mock theta conjectures==
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* conjecture by Andrews-Dragonette
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* Hickerson1988 http://worldcat.org/issn/0020-9910
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* [[Rank of partition and mock theta conjecture]]
  
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<h5>mock theta function</h5>
 
  
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* mock theta function is essentially a mock modular form of weight 1/2
 
  
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==examples==
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* classify which examples are of which use
  
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<h5>mock theta conjectures</h5>
 
  
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* <cite class="" id="CITEREFWatson1936" style="font-style: normal;">Watson, G. N. (1936), "The Final Problem : An Account of the Mock Theta Functions", <em style="">J. London Math. Soc.</em>'''11''': 55–80, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1112%2Fjlms%2Fs1-11.1.55 10.1112/jlms/s1-11.1.55]</cite>
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==mock theta functions==
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* <cite class="" id="CITEREFWatson1937" style="font-style: normal;">Watson, G. N. (1937), "The Mock Theta Functions (2)", <em style="">Proc. London Math. Soc.</em>'''s2-42''': 274–304, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1112%2Fplms%2Fs2-42.1.274 10.1112/plms/s2-42.1.274]</cite>
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* [[3rd order mock theta functions]]
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* [http://dx.doi.org/10.1016/0001-8708%2889%2990070-4 Ramanujan's “Lost” Notebook VI: The mock theta conjectures]<br>
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* [[5th order mock theta functions]]
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** George E. Andrews and F. G. Garvan   
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* [[7th order mock theta functions]]
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* <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>
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* [[8th order Mock theta functions]]
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* [[10th order mock theta functions]]
  
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<h5>order 3</h5>
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==other examples==
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* [[Appell-Lerch sums]]
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* characters of [[Kac-Wakimoto modules]]
  
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* <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>
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*  good introduction is given in Andrews article <br>
 
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** [http://www.ingentaconnect.com/content/klu/rama/2003/00000007/F0030001/05142410 Partitions : at the interface of q-series and modular forms]
 
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** [http://www.ingentaconnect.com/content/klu/rama/2003/00000007/F0030001/05142410 ]section 5
 
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* 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]).
 
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* 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.
 
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* [http://dx.doi.org/10.1112%2Fjlms%2Fs1-11.1.55 The Final Problem : An Account of the Mock Theta Functions]<br>
 
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** Watson, G. N. (1936)
 
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**  J. London Math. Soc. 11: 55–80
 
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* [http://dx.doi.org/10.2307%2F1990714 Some asymptotic formulae for the mock theta series of Ramanujan]<br>
 
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** Dragonette, Leila A. (1952), 
 
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** Transactions of the American Mathematical Society 72: 474–500
 
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* [http://dx.doi.org/10.2307%2F2373202 On the theorems of Watson and Dragonette for Ramanujan's mock theta functions]<br>
 
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** Andrews, George E. (1966)
 
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** American Journal of Mathematics 88: 454–490<br>
 
  
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==related items==
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* [[mock modular forms]]
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* [[Asymptotic analysis of modular forms]]
  
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<h5>order 5</h5>
 
  
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* G.E. Andrews, The fifth and seventh order mock theta functions. Trans. Amer. Math. Soc. 293 (1986), pp. 113–134
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==expositions==
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* <cite class="" id="CITEREFAndrews1988" style="font-style: normal;">Andrews, George E. (1988), "Ramanujan's fifth order mock theta functions as constant terms", <em style="">Ramanujan revisited (Urbana-Champaign, Ill., 1987)</em>,</cite>
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*  Basil Gordon, Richard J. McIntosh  [http://link.springer.com/chapter/10.1007%2F978-1-4614-0028-8_9 A Survey of Classical Mock Theta Functions]  
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* [http://www.springerlink.com/content/l5444w8085367833/?p=220d154603944b58b52d6566cbcbe9c3&pi=16 Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions]<br>
 
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** Basil Gordon and Richard J. Mcintosh
 
  
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<h5>order 7</h5>
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==books==
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* Ramanujan's Lost Notebook: Part I
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* Ramanujan's Lost Notebook: Part II
  
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* <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>
 
  
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==encyclopedia==
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<h5>order 10</h5>
 
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* <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>
 
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* <cite class="" id="CITEREFChoi2000" style="font-style: normal;">Choi, Youn-Seo (2000), "Tenth order mock theta functions in Ramanujan's lost notebook. II", <em style="">Advances in Mathematics</em>'''156''' (2): 180–285, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1006%2Faima.2000.1948 10.1006/aima.2000.1948], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=1808245 1808245], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0001-8708 0001-8708]</cite>
 
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* <cite class="" id="CITEREFChoi2002" style="font-style: normal;">Choi, Youn-Seo (2002), "[http://www.jstor.org/stable/2693766 Tenth order mock theta functions in Ramanujan's lost notebook. IV]", <em style="">[http://en.wikipedia.org/wiki/Transactions_of_the_American_Mathematical_Society Transactions of the American Mathematical Society]</em>'''354''' (2): 705–733, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1090%2FS0002-9947-01-02861-6 10.1090/S0002-9947-01-02861-6], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=1862564 1862564], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0002-9947 0002-9947], http://www.jstor.org/stable/2693766</cite>
 
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* <cite class="" id="CITEREFChoi2007" style="font-style: normal;">Choi, Youn-Seo (2007), "Tenth order mock theta functions in Ramanujan's lost notebook. III", <em style="">Proceedings of the London Mathematical Society. Third Series</em>'''94''' (1): 26–52, [http://en.wikipedia.org/wiki/Digital_object_identifier doi]:[http://dx.doi.org/10.1112%2Fplms%2Fpdl006 10.1112/plms/pdl006], [http://en.wikipedia.org/wiki/Mathematical_Reviews MR][http://www.ams.org/mathscinet-getitem?mr=2293464 2293464], [http://en.wikipedia.org/wiki/International_Standard_Serial_Number ISSN][http://worldcat.org/issn/0024-6115 0024-6115]</cite>
 
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[http://mathsci.ucd.ie/%7Ezwegers/papers/006.pdf http://mathsci.ucd.ie/~zwegers/papers/006.pdf]
 
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<h5>간단한 소개</h5>
 
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<h5>하위주제들</h5>
 
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==== 하위페이지 ====
 
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* [http://pythagoras0.springnote.com/pages/1964250 0 토픽용템플릿]<br>
 
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** [http://pythagoras0.springnote.com/pages/2060652 0 상위주제템플릿]<br>
 
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<h5>재미있는 사실</h5>
 
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<h5>관련된 단원</h5>
 
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<h5>많이 나오는 질문</h5>
 
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*  네이버 지식인<br>
 
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** http://kin.search.naver.com/search.naver?where=kin_qna&query=
 
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<h5>관련된 고교수학 또는 대학수학</h5>
 
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<h5>관련된 다른 주제들</h5>
 
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* [[mock modular forms|Mock modular forms]]
 
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<h5>표준적인 도서 및 추천도서</h5>
 
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* [http://gigapedia.com/items:links?id=38285 Ramanujan's Lost Notebook: Part I]
 
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* [http://gigapedia.com/items:links?id=294608 Ramanujan's Lost Notebook: Part II]
 
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* [[2009년 books and articles|찾아볼 수학책]]
 
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* http://gigapedia.info/1/Polyogarithms
 
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* http://gigapedia.info/1/ramanujan
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
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<h5>참고할만한 자료</h5>
 
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* http://www.zentralblatt-math.org/zmath/en/
 
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* http://ko.wikipedia.org/wiki/
 
 
* http://en.wikipedia.org/wiki/Mock_modular_form
 
* http://en.wikipedia.org/wiki/Mock_modular_form
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* http://viswiki.com/en/
 
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* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
 
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* 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=
 
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* 다음백과사전 http://enc.daum.net/dic100/search.do?q=
 
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<h5>이미지 검색</h5>
 
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* http://commons.wikimedia.org/w/index.php?title=Special%3ASearch&search=
 
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<h5>동영상</h5>
 
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* http://www.youtube.com/results?search_type=&search_query=
 
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<h5>관련기사</h5>
 
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네이버 뉴스 검색 (키워드 수정)
 
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* http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
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* http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
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* http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
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* http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
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* http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
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* http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
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<h5>블로그</h5>
 
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* 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
 
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* 트렌비 블로그 검색 http://www.trenb.com/search.qst?q=
 
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[[분류:개인노트]]
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[[분류:math and physics]]
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[[분류:mock modular forms]]
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[[분류:math]]
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[[분류:migrate]]
  
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<h5>TeX 작업</h5>
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q3754575 Q3754575]
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===Spacy 패턴 목록===
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* [{'LOWER': 'mock'}, {'LOWER': 'modular'}, {'LEMMA': 'form'}]

2021년 2월 17일 (수) 02:10 기준 최신판

introduction

  • mock theta function is essentially a holomorphic part of Mock modular forms of weight 1/2
  • Ramanujan found 17 examples



mock theta conjectures


examples

  • classify which examples are of which use


mock theta functions


other examples


related items


expositions


books

  • Ramanujan's Lost Notebook: Part I
  • Ramanujan's Lost Notebook: Part II


encyclopedia

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'mock'}, {'LOWER': 'modular'}, {'LEMMA': 'form'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Examples_of_mock_modular_forms&oldid=51695"