# Tagged Questions

683 views

### Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?

QUESTION I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to complex logarithm is ...
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### Relations between automorphisms of field of rational functions and Mobius Transfomation

Proposition: If $F$ is a field, let $F[x]$ be the ring of all polynomials whose coefficients are in $F$. The fraction field of $F[x]$, denoted $F(x)$, is defined to be the ratios $r(x) = f(x)/g(x)$ ...
868 views

### If a formal power series over the complex numbers satisfies a polynomial identity, does it imply that the power series has a radius of convergence?

Let $P(z)$ be a $\textit{formal}$ power series in $z$ that a priori may not have a non zero radius of convergence. Assume that $P(0) =0$. Let $\Phi(w,z)$ be a polynomial in two variables, that ...
Hi, everyone! I'm trying to explain the proof of Luroth theorem (every field $L$, s.t. $K\subset L\subset K(t)$, is isomorphic to $K(t)$) to the high-school audience. I'm not going to use such ...
Consider a complex polynomial map $f: \mathbb{C}^n \rightarrow \mathbb{C}^n$. For $n = 1$, the fundamental theorem of algebra says that, for any $y \in \mathbb{C}$ there exists $x \in \mathbb{C}$ ...