# Questions tagged [elliptic-functions]

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35 questions
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### Elliptic units and Euler system

Maybe this question is quite obscure and ambiguous. I am really sorry for such ambiguity. My question is, what is the good thing we get from defining elliptic units and Euler system? There are lots ...
1answer
227 views

### A proof of energy functional appearing in the regularity of elliptic and parabolic equations

I have got trapped in this problem for nearly two years when I dealt with regularity of solutions of elliptic and parabolic equations. I have not found a nice proof to support this assertion. Now I am ...
1answer
387 views

### Are traditional notations for elliptic integrals/functions in Latin or Greek letters?

I am doing some calculation involving elliptic integrals/functions, and find the notations confusing. In Wittaker-Watson, the "Jacobi's earlier notation" H(u) is called the Eta-function, so the "H" ...
1answer
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### Evaluating the average distance from a point in the unit disk to the disk

I am interested in finding the average Euclidean distance from a point $(x,y)\in\mathbb{D}_2$, the unit disk $\{(u,v):u^2+v^2\leq 1\}\subseteq\mathbb{R}^2$, to the disk $\mathbb{D}_2$. This amounts to ...
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### Mathematician, Graciano Ricalde

Does anyone understand more precisely how to explain the 5th degree equation and elliptic functions accomplishments of Mathematician Graciano Ricalde? I am his great grand-daughter and trying to ...
2answers
613 views

### Special values of a doubly periodic meromorphic function

Consider the following function: $G(z) = \prod_{n \in \mathbb{Z}} {1 \over{\tanh^2\left(\pi\left(z-n\right)\right)}}$. By constuction, it has poles at $z=m+in$ with $m,n \in \mathbb{Z}^2$. ...
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### Convexity of Jacobi's theta function with zero argument

This question may be elementary, I have asked it on math.stackexchange.com but have not received any answer yet. Note that I am not an expert on theta/elliptic functions. Define Jacobi's theta ...
3answers
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### question about the recursion equation: $x_{n+1}x_{n−1}=x_n^2(1−4x_n)$

Hi all, I am trying to slove the recursion equation: $x_{n+1}x_{n−1}=x_n^2(1−4x_n)$ in the form of $x_n=x_n(x_1,x_2)$ or $x_n=x_n(c_1,c_2)$, and finally get the limit of the ratio: \$\dfrac{x_n}{x_{n+...
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### Proofs of Jacobi's four-square theorem

What are the nicest proofs of Jacobi’s four-square theorem you know? How much can they be streamlined? How are they related to each other? I know of essentially three aproaches. Modular forms, as in,...