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The Fourier-Stieltjes transform of Minkowski's ?(x) function and an affirmative answer to Salem's problem

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Semyon Yakubovich

Classical Analysis and ODEs · Submitted 21 Mar 2011

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

The authors' main claim This paper is substituted with a correct alternative and affirmative solution of Salem's problem and its generalization for derivatives of any order of the Fourier-Stieltjes transform of the Minkowski'i question mark function.

how it is stated · asserted 0.99 read the record →

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arXiv ID1103.3979 (version 2)
Pith IDIA5VM2VV, Pith's permanent record of this paper and its review
CitationSemyon Yakubovich. "The Fourier-Stieltjes transform of Minkowski's ?(x) function and an affirmative answer to Salem's problem." arXiv:1103.3979 (2011). https://pith.science/paper/IA5VM2VV
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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, 3,633 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.37 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

By using structural and asymptotic properties of the Kontorovich-Lebedev transform associated with Minkowski's question mark function, we give an affirmative answer to the question posed by R. Salem (Trans. Amer. Math. Soc., 53 (3), (1943), p. 439) whether its Fourier-Stieltjes transform vanishes at infinity. This paper is substituted with a correct alternative and affirmative solution of Salem's problem and its generalization for derivatives of any order of the Fourier-Stieltjes transform of the Minkowski'i question mark function. The question is finally solved.

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 By using structural and asymptotic properties of the Kontorovich-Lebedev transform associated with Minkowski's question mark function, we give an affirmative answer to the question posed by R. Salem (Trans. Amer. Math. contribution 0.55 0.89 0.33 asserted 1.00
s1 Soc., 53 (3), (1943), p. 439) whether its Fourier-Stieltjes transform vanishes at infinity. result 0.45 0.29 0.50 asserted 0.74
s2 This paper is substituted with a correct alternative and affirmative solution of Salem's problem and its generalization for derivatives of any order of the Fourier-Stieltjes transform of the Minkowski'i question mark function. contribution 0.86 0.79 0.50 asserted 0.99
s3 The question is finally solved. result 0.75 0.63 0.23 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

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  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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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

By using structural and asymptotic properties of the Kontorovich-Lebedev transform associated with Minkowski's question mark function, we give an affirmative answer to the question posed by R. Salem (Trans. Amer. Math. Soc., 53 (3), (1943), p. 439) whether its Fourier-Stieltjes transform vanishes at infinity. This paper is substituted with a correct alternative and affirmative solution of Salem's problem and its generalization for derivatives of any order of the Fourier-Stieltjes transform of the Minkowski'i question mark function. The question is finally solved.

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