# Questions tagged [cv.complex-variables]

Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

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### Two questions on asymptotic expansion of confluent hypergeometric functions for real variable $x, |x| \to \infty$

I'm looking into the asymptotic expansion for confluent hypergeometric function $_1F_1(a;b;z) \equiv M(a;b;z)$ and I've two quick questions regarding its asymptotic behavior for real values $x,$ i.e. ...
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### Real integrals with complex analysis [closed]

I don't have a clear formal viewpoint on this problem. Resolving the Euler-Lagrange equations for the string with a point mass perturbation: $$\frac{\partial^2 \phi }{\partial x^2} = \delta (x-a)$$ I ...
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### What can be concluded from the analyticity in a half-plane of a sum of functions?

If I have two functions $F$ and $G$ for which $F(s)+G(s)$ is analytic in some half-plane ${\rm Re}(s)>a$, what can be concluded about these functions individually with respect to their analyticity? ...
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### Does the maximum principle hold in this pluriharmonic setting?

Let $U \subseteq \mathbb{C}^m$ be open, and let $F: U \to \mathbb{C}$ be a holomorphic function, with real part $u$. We are given a subset $S \subseteq U$ given by finitely many real equalities and ...
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### Regarding supremum over a set

Let $\Delta$ be a Compact Hausdorff space in $\mathbb{C^n}$. Let $A$ be a closed sub algebra of $C(\Delta)$(space of all complex valued continuous functions on $\Delta$) which contains the constant ...
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### Holomorphic function bounded in a sector with angle $>\pi$ [closed]

I know that according to Liouville’s theorem, if a holomorphic function is bounded on all of C, it is constant. This got me thinking if I could find holomorphic non-constant functions that are bounded ...
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### Short research articles

I am a masters student. I am interested in short articles which have counter examples and very few references. I want to write a short and interesting article. For example; One of the best known ...
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### Extension to all dimensions of complex line integral

Let $\Gamma$ be a smooth curve in $\mathbb{C}^d$. Since $\mathbb{C}^d$ can be seen as $\mathbb{R}^{2d}$, one can define the line integral of functions $f:\Gamma\to \mathbb{C}$ using for instance ...
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### When are two complex Tori biholomorphic

Let $g \ge 1$ be a natural number and $\mathbb{C}^g$ complex vector space which is isomorphic to $\mathbb{R}^{2g}$ is real vector space. An additive subgroup $\Gamma \subset \mathbb{C}^g$ is called a ...