Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Simplifications in Basic Complex Analysis   This paper presents very simple and easy integration-free proofs in the
context of Weierstrass's theory of functions, of the Maximum and Minimum
Modulus Principles and Gutzmer-Parseval Inequalities for polynomials and for
functions developable in complex power series at every point in their domains,
as well as a trivial proof of the Open Mapping Theorem, an intuitive version of
Liouville's Theorem, an easy proof of Weierstrass's Theorem on Double Series, a
modest extension of Schwarz's Lemma, and some other related results. It also
presents easy proofs of the P\'olya-Szeg\"o and P. Erd\"os' Anti-Calculus
Proposition, a theorem on saddle points by Bak-Ding-Newman, and the well-known
Clunie-Jack Lemma.

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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org