Recherches sur les fonctions elliptiques
E64057
Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Recherches sur les fonctions elliptiques canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T511417 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Recherches sur les fonctions elliptiques Context triple: [Niels Henrik Abel, notableWork, Recherches sur les fonctions elliptiques]
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A.
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
-
B.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
C.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
D.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
-
E.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Recherches sur les fonctions elliptiques Target entity description: Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
-
A.
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
-
B.
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe
Über die Darstellbarkeit einer Funktion durch eine trigonometrische Reihe is Bernhard Riemann’s seminal 1854 paper that laid foundational ideas for Fourier series and modern real analysis, including the concept now known as the Riemann integral.
-
C.
Über die Bildung des Formensystems der ternären biquadratischen Form
"Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
-
D.
Théorie analytique de la chaleur
Théorie analytique de la chaleur is Joseph Fourier’s foundational 1822 treatise that introduced Fourier series and laid the mathematical groundwork for the modern theory of heat conduction and harmonic analysis.
-
E.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
- F. None of above. chosen
Statements (31)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical treatise
ⓘ
scientific publication ⓘ |
| author | Niels Henrik Abel ⓘ |
| authorNationality | Norwegian ⓘ |
| contributedTo |
development of the theory of elliptic functions
ⓘ
foundations of modern complex analysis ⓘ |
| field |
complex analysis
ⓘ
mathematics ⓘ |
| genre | research monograph ⓘ |
| hasAuthorContribution | Abel’s major work on elliptic and Abelian functions ⓘ |
| hasContribution |
clarified the inversion of elliptic integrals
ⓘ
established addition theorems for elliptic functions ⓘ introduced general methods for transcendental functions ⓘ |
| historicalPeriod | early 19th century mathematics ⓘ |
| impact |
considered a foundational work in the theory of elliptic functions
ⓘ
helped shape the modern concept of complex analytic functions ⓘ |
| influenced |
Bernhard Riemann
ⓘ
Carl Gustav Jacob Jacobi ⓘ development of Abelian functions ⓘ theory of Riemann surfaces ⓘ |
| influencedBy | earlier work on elliptic integrals ⓘ |
| language | French ⓘ |
| mainSubject | elliptic functions ⓘ |
| namedAfter | elliptic functions ⓘ |
| notableFor |
influence on later work in algebraic geometry
ⓘ
introduction of Abelian integrals concepts ⓘ systematic study of elliptic functions ⓘ |
| originalTitleLanguage | French ⓘ |
| partOf | 19th-century literature on analysis ⓘ |
| publicationCentury | 19th century ⓘ |
| title | Recherches sur les fonctions elliptiques ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Recherches sur les fonctions elliptiques Description of subject: Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.