# Tagged Questions

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### Integration over subsets of the complex plane.

Original Problem: Let $\Omega\subset \mathbb{C}$ be an open set and let $f:\Omega\to\mathbb{C}$ be holomorphic such that $f\in L^{2}(\Omega)$. Show that if $B(z,r)$, the ball of radius $r$ ...
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### when does bijective map exist for any pair of rational function?

Let me ask kind of different questions than former ones. Given $$\frac{P_1(x_1,x_2,\dots,x_n)}{P_2(x_1,x_2,\dots,x_n)}\text{, and }\frac{P_3(y_1,y_2,\dots,y_n)}{P_4(y_1,y_2,\dots,y_n)}$$ where $P_i$ ...
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### A question on the 2-norm defined by $||x||_2=\sqrt{\sum\limits_{i=1}^n|x_i|^2}$

A question on the 2-norm defined by $||x||_2=\sqrt{\sum\limits_{i=1}^n|x_i|^2}$ I am trying to prove the triangle inequality of this norm. So far I have that: \begin{align} ...
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### Is $\sum c_n z^n$ analytic when $c_n$ is Banach-valued?

I'm trying to define "Analytic function". I want a definition that covers all interesting cases. To be specific, let me explain what exactly I want Here is the definition of analytic function in ...
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### Question about the zeros of $\zeta_{H}(s,a) \pm \zeta_{H}(s,1-a)$.

Assume $\zeta_{H}(s,a)$ is the Hurwitz Zeta function. Note that for $a=\frac13,\frac14,\frac16$ the zeros of: $$\zeta_{H}(s,a) + \zeta_{H}(s,1-a)$$ are the same as the non-trivial zeros $\rho$ of ...
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