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DedekindEta

Usage

DedekindEta[ ] 给出 Dedekind eta 模椭圆函数Eta(Tau)


Notes

• 数学函数(参见 A.3.10).
DedekindEta仅在复平面的上半平面有定义.对实数  ,它也没有定义.
• 参数  是Weierstrass 半周期的比值 .
DedekindEta满足   是判别式,它根据不变量由  给出.
• 参见 3.2.11 节中对椭圆函数参数约定的讨论.
•参见 Mathematica 全书: 3.2.11节.
Further Examples

The Dedekind eta function  is defined by  , for  in the complex upper half-plane. If  is regarded as the ratio of half-periods of an elliptic curve and  are the corresponding Weierstrass coefficients, then  .

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Under fractional linear transformations of the complex plane with integer coefficients, the Dedekind eta function transforms in simple ways. The most obvious example of such a transformation (apart from the identity) is  ; in this case  .

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In[3]:=  

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In[4]:=