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

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imported>Pythagoras0
imported>Pythagoras0
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==mock theta functions== 
 
 
==order 3==
 
 
 
 
* [[3rd order mock theta functions]]
 
* [[3rd order mock theta functions]]
 
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* [[5th order mock theta functions]]
 
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* [[7th 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
 
* <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>
 
* [http://www.springerlink.com/content/l5444w8085367833/?p=220d154603944b58b52d6566cbcbe9c3&pi=16 Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions]<br>
 
** Basil Gordon and Richard J. Mcintosh
 
 
 
 
 
 
 
==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>
 
 
 
 
 
 
 
 
 
 
 
==order 8==
 
 
 
 
* [[8th order Mock theta functions]]
 
* [[8th order Mock theta functions]]
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* [[10th order mock theta functions]]
  
 
 
 
 
 
  
==order 10==
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==other examples==
* [[10th order mock theta functions]]
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* [[Appell-Lerch sums]]
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* characters of [[Kac-Wakimoto modules]]
  
 
 
 
 

2013년 3월 17일 (일) 16:42 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


examples

  • classify which examples are of which use

 

==mock theta functions== 


other examples

 

related items

 

books

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


encyclopedia