Tagged Questions
0
votes
0answers
30 views
References for the conformal equivalence of the space of complex 1-tori and C?
What are some good references with proofs of the conformal equivalence of the space of complex tori and $\mathbb{C}$? So far I only have the book by Jones and Singerman.
14
votes
1answer
238 views
The importance of modular forms
I'm studying modular forms and my professor started the course talking about elliptic functions. These particular functions form a field (once that the lattice $\Lambda$ is fixed) called ...
3
votes
0answers
107 views
Weierstrass $\wp$-Function Addition Property
Consider the function
$$
\det\left( \begin{array}{ccccc}
&1 &\wp(z) &\wp'(z) \\
&1 &\wp(w) &\wp'(w) \\
&1 &\wp(-z-w) &\wp'(-z-w) \end{array} \right)=f(z)
$$
I'm ...
0
votes
0answers
78 views
Why is Every Elliptic Function of Order $2$ the Möbius Tranform of a $\wp$-function?
I'm trying to prove that every elliptic function of order $2$ has the form
$$f(z)=\frac{a\wp(z-z_0)+b}{c\wp(z-z_0)+d}$$
I've got the following so far. Let $f$ be an elliptic function of order 2. ...
3
votes
0answers
97 views
Equivalent Definitions of the Weierstass $\wp$-Function
I've come across two equivalent definitions of the Weierstrass $\wp$-function, but don't know how to prove that they are equivalent.
Definition 1
$\wp(z)=cf(z)+d$ where $f$ is the elliptic function ...
4
votes
1answer
625 views
A Torus and the Weierstrass P function?
In case you don't know what I'm talking about:
http://en.wikipedia.org/wiki/Weierstrass%27s_elliptic_functions
I'm reading Farkas and Kra's "Riemann Surfaces," and they talk briefly about these guys ...
