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

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<h5>order 3</h5>
 
<h5>order 3</h5>
  
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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>
 
* 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]).
 
* 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.
 
* 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/10.2307%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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*   <br>
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** <br>
  
 
 
 
 
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* http://www.zentralblatt-math.org/zmath/en/
 
* http://www.zentralblatt-math.org/zmath/en/
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*  
 
 
* http://ko.wikipedia.org/wiki/
 
* http://ko.wikipedia.org/wiki/
 
* http://en.wikipedia.org/wiki/Mock_modular_form
 
* http://en.wikipedia.org/wiki/Mock_modular_form

2009년 8월 9일 (일) 01:21 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

 

order 3
  • \(f(q) = \sum_{n\ge 0} {q^{n^2}\over (-q;q)_n^2} = {2\over \prod_{n>0}(1-q^n)}\sum_{n\in Z}{(-1)^nq^{3n^2/2+n/2}\over 1+q^n}\)
  • 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.
  • Some asymptotic formulae for the mock theta series of Ramanujan
    • Dragonette, Leila A. (1952), 
    • Transactions of the American Mathematical Society 72: 474–500
  •  

 

order 5

 

order 7

 

 

order 10

http://mathsci.ucd.ie/~zwegers/papers/006.pdf

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