The tag has no wiki summary.

learn more… | top users | synonyms

1
vote
1answer
204 views

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 ...
2
votes
1answer
171 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 ...
0
votes
0answers
48 views

Significance of a combination of Weierstrass zeta values arising in the Lagrange top

I'll follow the notation of Whittaker and Watson. Let $\zeta(z)$ be the Weierstrass zeta function with half periods $\omega_{1,2}$ and $\eta_i=\zeta(\omega_i)$. I am interested in the case where the ...
2
votes
1answer
145 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" ...
6
votes
1answer
299 views

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 ...
26
votes
2answers
2k views

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 ...
2
votes
2answers
459 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 $m,n \in \mathbb{Z}^2$. ...
9
votes
0answers
549 views

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 ...
4
votes
3answers
493 views

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: ...
13
votes
5answers
1k views

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 ...