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Minorations simultan\'ees de formes lin\'eaires de logarithmes de nombres alg\'ebriques

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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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Éric Gaudron (IF)

Number Theory · Submitted 21 Apr 2010

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

The authors' main claim We give lower bounds for simultaneous linear forms in logarithms of algebraic numbers, treating both the archimedean and $p$-adic cases.

how it is stated · asserted 1.00 read the record →

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arXiv ID1004.3652 (version 3)
Pith IDNGMDLZEW, Pith's permanent record of this paper and its review
Citation\'Eric Gaudron (IF). "Minorations simultan\'ees de formes lin\'eaires de logarithmes de nombres alg\'ebriques." arXiv:1004.3652 (2010). https://pith.science/paper/NGMDLZEW
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,574 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.24 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

This work falls within the theory of linear forms in logarithms over a commutative linear group defined over a number field. We give lower bounds for simultaneous linear forms in logarithms of algebraic numbers, treating both the archimedean and $p$-adic cases. The proof includes Baker's method, Hirata's reduction, Chudnovsky's process of variable change. The novelty is that we integrated into the proof the modern tools of adelic slope theory, using also a new small values Siegel's lemma.

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 This work falls within the theory of linear forms in logarithms over a commutative linear group defined over a number field. background 1.00 0.16 0.04 asserted 1.00
s1 We give lower bounds for simultaneous linear forms in logarithms of algebraic numbers, treating both the archimedean and $p$-adic cases. contribution 0.55 0.94 0.83 asserted 1.00
s2 The proof includes Baker's method, Hirata's reduction, Chudnovsky's process of variable change. method 1.00 0.42 0.04 asserted 1.00
s3 The novelty is that we integrated into the proof the modern tools of adelic slope theory, using also a new small values Siegel's lemma. contribution 1.00 0.91 0.13 asserted 1.00

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

sources read
  • arXiv listing abstract v3
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

This work falls within the theory of linear forms in logarithms over a commutative linear group defined over a number field. We give lower bounds for simultaneous linear forms in logarithms of algebraic numbers, treating both the archimedean and $p$-adic cases. The proof includes Baker's method, Hirata's reduction, Chudnovsky's process of variable change. The novelty is that we integrated into the proof the modern tools of adelic slope theory, using also a new small values Siegel's lemma.

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