Vorlesungen über Zahlentheorie (with Dirichlet)
E634840
Vorlesungen über Zahlentheorie (with Dirichlet) is a foundational 19th-century textbook on number theory, based on lectures by Peter Gustav Lejeune Dirichlet and edited and expanded by Richard Dedekind.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Vorlesungen über Zahlentheorie (with Dirichlet) canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7011060 — 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: Vorlesungen über Zahlentheorie (with Dirichlet) Context triple: [Richard Dedekind, notableWork, Vorlesungen über Zahlentheorie (with Dirichlet)]
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A.
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.
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B.
Theorie der algebraischen Zahlen
"Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
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C.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
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D.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
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E.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
- 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: Vorlesungen über Zahlentheorie (with Dirichlet) Target entity description: Vorlesungen über Zahlentheorie (with Dirichlet) is a foundational 19th-century textbook on number theory, based on lectures by Peter Gustav Lejeune Dirichlet and edited and expanded by Richard Dedekind.
-
A.
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.
-
B.
Theorie der algebraischen Zahlen
"Theorie der algebraischen Zahlen" is Kurt Hensel’s foundational work in algebraic number theory, notable for introducing and developing the concept of p-adic numbers.
-
C.
Die Theorie der algebraischen Zahlkörper
"Die Theorie der algebraischen Zahlkörper" is a foundational mathematical monograph on algebraic number fields, authored by David Hilbert and published as part of his influential Zahlbericht.
-
D.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
-
E.
Three Pearls of Number Theory
Three Pearls of Number Theory is a classic mathematical text that presents three elegant and accessible problems in number theory, illustrating deep ideas through simple, beautifully explained examples.
- F. None of above. chosen
Statements (37)
| Predicate | Object |
|---|---|
| instanceOf |
19th-century book
ⓘ
mathematics book ⓘ number theory textbook ⓘ |
| academicDiscipline | pure mathematics ⓘ |
| associatedWith |
Dirichlet L-functions
NERFINISHED
ⓘ
Dirichlet characters NERFINISHED ⓘ Dirichlet’s theorem on primes in arithmetic progressions NERFINISHED ⓘ |
| author | Peter Gustav Lejeune Dirichlet NERFINISHED ⓘ |
| basedOn | lectures by Peter Gustav Lejeune Dirichlet ⓘ |
| contributor |
Peter Gustav Lejeune Dirichlet
NERFINISHED
ⓘ
Richard Dedekind NERFINISHED ⓘ |
| countryOfOrigin | Germany ⓘ |
| editor | Richard Dedekind NERFINISHED ⓘ |
| editorAddedSectionsOn | ideal theory and algebraic number theory ⓘ |
| editorExpandedContent | Richard Dedekind NERFINISHED ⓘ |
| fieldOfStudy |
mathematics
ⓘ
number theory ⓘ |
| genre |
lecture notes
ⓘ
textbook ⓘ |
| hasEditorRole | Richard Dedekind NERFINISHED ⓘ |
| hasLecturerRole | Peter Gustav Lejeune Dirichlet NERFINISHED ⓘ |
| hasPart |
proof of Dirichlet’s theorem on arithmetic progressions
ⓘ
treatment of Dirichlet L-series ⓘ treatment of Dirichlet characters ⓘ treatment of arithmetic of integers ⓘ treatment of congruences ⓘ treatment of quadratic forms ⓘ |
| historicalSignificance | foundational work in modern number theory ⓘ |
| influenced |
development of algebraic number theory
ⓘ
later number theory textbooks ⓘ |
| language | German ⓘ |
| mainSubject | number theory ⓘ |
| notableFor |
historical importance in 19th-century number theory
ⓘ
rigorous treatment of analytic number theory topics ⓘ systematic presentation of Dirichlet’s methods ⓘ |
| timePeriod | 19th century ⓘ |
| titleLanguage | German ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Vorlesungen über Zahlentheorie (with Dirichlet) Description of subject: Vorlesungen über Zahlentheorie (with Dirichlet) is a foundational 19th-century textbook on number theory, based on lectures by Peter Gustav Lejeune Dirichlet and edited and expanded by Richard Dedekind.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.