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Multiplicative structures of values of the sum-of-divisors function

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Tomohiro Yamada

Number Theory · Submitted 8 Dec 2005

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

The authors' main claim We shall improve upper bounds for the size and the number of solutions of such equations.

how it is stated · asserted 0.89 read the record →

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arXiv IDmath/0512175 (version 1)
Pith IDMZONO4I5, Pith's permanent record of this paper and its review
CitationTomohiro Yamada. "Multiplicative structures of values of the sum-of-divisors function." arXiv:math/0512175 (2005). https://pith.science/paper/MZONO4I5
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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, 2,307 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.39 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We study equations of the form $\sigma(p^{q-1})=Az$, where $p$ is a prime, $q$ is a fixed odd prime, $A$ is a fixed integer and $z$ is an integer composed of primes in a fixed finite set. We shall improve upper bounds for the size and the number of solutions of such equations.

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 study equations of the form $\sigma(p^{q-1})=Az$, where $p$ is a prime, $q$ is a fixed odd prime, $A$ is a fixed integer and $z$ is an integer composed of primes in a fixed finite set. background 0.54 0.45 0.05 asserted 0.71
s1 We shall improve upper bounds for the size and the number of solutions of such equations. contribution 0.81 0.70 0.40 asserted 0.89

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

What was examined, and what was not

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  • references and citing sentences
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  • 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

We study equations of the form $\sigma(p^{q-1})=Az$, where $p$ is a prime, $q$ is a fixed odd prime, $A$ is a fixed integer and $z$ is an integer composed of primes in a fixed finite set. We shall improve upper bounds for the size and the number of solutions of such equations.

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