Timeline for Understanding Umemura's Theorem for roots of algebraic equations
Current License: CC BY-SA 3.0
10 events
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| Oct 15, 2022 at 14:03 | answer | added | Student | timeline score: 1 | |
| Feb 19, 2017 at 1:34 | comment | added | Fan Zheng | But I'm confused for two different reasons: 1. How do you get $x_k$ for a different $k$? 2. In all invocation of the $\theta$ function, $m_1$ is always in $\mathbb{Z}^g$, so do we still need $m_1$ in this case? It seems that it can be absorbed by a change of variable $\xi+m_1\mapsto\xi$. | |
| Feb 19, 2017 at 1:31 | comment | added | Fan Zheng | Why does the equation give a matrix? It seems to me to give a scalar. | |
| S Feb 18, 2017 at 22:38 | history | suggested | IV_ | CC BY-SA 3.0 |
I replaced the dead link.
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| Feb 18, 2017 at 22:01 | review | Suggested edits | |||
| S Feb 18, 2017 at 22:38 | |||||
| Dec 13, 2013 at 12:13 | comment | added | George Lazou | I apologise, no one seems interested in this question. But for completeness sake, in answer to the first question, it seems that for Riemann Theta functions we define $n \cdot \Omega \cdot n = \Sigma_{i, j = 1}^{g} \Omega_{ij}n_{i}n_{j}$ giving a scalar, where $n \in \mathbb{Z}^{g}$ and $\Omega \in \mathbb{C}^{g \times g}$. I assume $(\xi + m_{1})^{T}(z + m_{2})$ is just the dot product also giving a scalar. | |
| Dec 12, 2013 at 15:01 | comment | added | George Lazou | I found the original paper of Umemura online so have edited the question to take this into account. I am still struggling to understand, but I think everything is there, if someone would be kind enough to explain. | |
| Dec 12, 2013 at 14:59 | history | edited | George Lazou | CC BY-SA 3.0 |
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| Dec 11, 2013 at 19:07 | history | edited | George Lazou | CC BY-SA 3.0 |
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| Dec 11, 2013 at 14:09 | history | asked | George Lazou | CC BY-SA 3.0 |