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Results tagged with cv.complex-variables
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user 22971
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
5
votes
Accepted
Exact reference for Liouville theorem
Is it possible that the Liouville theorem you are thinking of is the boundedness theorem, whereas the result you have in mind is from a different paper of Liouville's? In particular, the paper:
Li …
- 7,831
12
votes
4
answers
2k
views
Seeking a Geometric Proof of a Generalized Alternating Series' Convergence
Let $z \in \mathbb{C} \backslash \lbrace 1 \rbrace$ with $|z| = 1$. We consider the following infinite series, which necessarily converges:
$$S(z) := \sum_{n = 1}^{\infty}\frac{z^n}{n}$$
Note that $S …
- 7,831
11
votes
1
answer
1k
views
Extending an assignment property from Q to R (or C)
Property of any odd number of nonnegative integers:
Given $x_1 \leq \cdots \leq x_{2n + 1}$ with each $x_i \in \mathbb{Z}_{\geq 0}$, suppose that for any $x_i$ we remove, the remaining numbers can be …
- 7,831
20
votes
Accepted
Are there irreducible polynomials with all zeros on two concentric circles?
Dubickas and Smyth (On the Remak Height, the Mahler Measure and Conjugate Sets of Algebraic Numbers Lying on Two Circles, 2001) discuss what they call extended Salem numbers.
Moreover, they present r …
- 7,831
9
votes
Accepted
On a paper by Dimitrie Pompéiu and on one (in two parts) by Edmund Landau
Below are both references: links then screenshots.
The first reference can be found in full here.
In case permissions etcetera should change, below are screenshots of the pages:
The second refe …
- 7,831