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Zeros, growth and Taylor coefficients of entire solutions of linear $q$-difference equations

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Walter Bergweiler

Complex Variables · Submitted 20 Dec 2019

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

The authors' main claim We use this to show that under a suitable hypothesis on the associated Newton-Puiseux diagram their zeros are asymptotic to finitely many geometric progressions.

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arXiv ID1912.09897 (version 2)
Pith IDG5L25GFR, Pith's permanent record of this paper and its review
CitationWalter Bergweiler. "Zeros, growth and Taylor coefficients of entire solutions of linear $q$-difference equations." arXiv:1912.09897 (2019). https://pith.science/paper/G5L25GFR
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,901 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.44 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.78 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider transcendental entire solutions of linear $q$-difference equations with polynomial coefficients and determine the asymptotic behavior of their Taylor coefficients. We use this to show that under a suitable hypothesis on the associated Newton-Puiseux diagram their zeros are asymptotic to finitely many geometric progressions. We also sharpen previous results on the growth rate of entire solutions.

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 We consider transcendental entire solutions of linear $q$-difference equations with polynomial coefficients and determine the asymptotic behavior of their Taylor coefficients. contribution 0.96 0.95 0.24 asserted 1.00
s1 We use this to show that under a suitable hypothesis on the associated Newton-Puiseux diagram their zeros are asymptotic to finitely many geometric progressions. result 0.95 0.94 0.39 asserted 1.00
s2 We also sharpen previous results on the growth rate of entire solutions. contribution 0.58 0.92 0.10 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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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

We consider transcendental entire solutions of linear $q$-difference equations with polynomial coefficients and determine the asymptotic behavior of their Taylor coefficients. We use this to show that under a suitable hypothesis on the associated Newton-Puiseux diagram their zeros are asymptotic to finitely many geometric progressions. We also sharpen previous results on the growth rate of entire solutions.

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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

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