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Power Series in Several Complex Variables

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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G. P. Balakumar

Complex Variables · Submitted 3 Jan 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.

how it is stated · asserted 0.89 read the record →

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arXiv ID1601.00274 (version 4)
Pith IDQUGJWE6K, Pith's permanent record of this paper and its review
CitationG. P. Balakumar. "Power Series in Several Complex Variables." arXiv:1601.00274 (2016). https://pith.science/paper/QUGJWE6K
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,602 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.33 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.12 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity. contribution 0.97 0.38 0.21 asserted 0.89

What kind of paper the classifier reports this is: review 0.92 · evidence from proof or derivation 0.81.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.

Human review

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How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Contests it 1 paper
  • Grigorchuk of the Texas A&M University for asking some doubts about certain erroneous points in an earlier expository article on power series of mine [ref] , which first provided the impetus to set them right and then develop it further into this article.

    Structure theorems for Power Series in Several Complex Variables · Introduction. · contest 0.89

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