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Sur l'autocorrelation multiplicative de la fonction "partie fractionnaire"

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Luis Baez-Duarte, Michel Balazard, Bernard Landreau, Eric Saias

Number Theory · Submitted 17 Jun 2003

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

The authors' main claim A first encounter with $A(\lambda) := \int_0^{+\infty}\{\lambda t\}\{t\}t^{-2}dt.$ This text contains the detailed calculations leading to the results of our paper "Etude de l'autocorrelation multiplicative de la fonction "partie fractionnaire"", to appear in the Ramanujan Journal.

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arXiv IDmath/0306251 (version 1)
Pith ID6EOCKSO2, Pith's permanent record of this paper and its review
CitationBernard Landreau, Eric Saias, Luis Baez-Duarte, Michel Balazard. "Sur l'autocorrelation multiplicative de la fonction "partie fractionnaire"." arXiv:math/0306251 (2003). https://pith.science/paper/6EOCKSO2
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,766 input tokens.

What the abstract itself states, as probabilities: claims first 0.39 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A first encounter with $A(\lambda) := \int_0^{+\infty}\{\lambda t\}\{t\}t^{-2}dt.$ This text contains the detailed calculations leading to the results of our paper "Etude de l'autocorrelation multiplicative de la fonction "partie fractionnaire"", to appear in the Ramanujan Journal.

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 A first encounter with $A(\lambda) := \int_0^{+\infty}\{\lambda t\}\{t\}t^{-2}dt.$ This text contains the detailed calculations leading to the results of our paper "Etude de l'autocorrelation multiplicative de la fonction "partie fractionnaire"", to appear in the Ramanujan Journal. contribution 0.73 0.83 0.08 asserted 0.74

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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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

A first encounter with $A(\lambda) := \int_0^{+\infty}\{\lambda t\}\{t\}t^{-2}dt.$ This text contains the detailed calculations leading to the results of our paper "Etude de l'autocorrelation multiplicative de la fonction "partie fractionnaire"", to appear in the Ramanujan Journal.

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