Basic Number Theory
E244837
Basic Number Theory is a foundational graduate-level text by André Weil that systematically develops algebraic number theory and related concepts with exceptional rigor and depth.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Basic Number Theory canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T2228029 — 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: Basic Number Theory Context triple: [André Weil, notableWork, Basic Number Theory]
-
A.
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.
-
B.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
-
C.
Fermat's little theorem
Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
-
D.
The Higher Arithmetic
The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
-
E.
Unsolved Problems in Number Theory
*Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
- 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: Basic Number Theory Target entity description: Basic Number Theory is a foundational graduate-level text by André Weil that systematically develops algebraic number theory and related concepts with exceptional rigor and depth.
-
A.
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.
-
B.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
-
C.
Fermat's little theorem
Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
-
D.
The Higher Arithmetic
The Higher Arithmetic is a classic introductory textbook on number theory, widely regarded for its clear exposition and influence on generations of mathematicians.
-
E.
Unsolved Problems in Number Theory
*Unsolved Problems in Number Theory* is a classic reference book that surveys a wide range of open questions and conjectures in number theory, often with historical context and extensive bibliographic notes.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics textbook ⓘ |
| author | André Weil ⓘ |
| edition | first edition ⓘ |
| emphasizes |
adelic and idelic methods
ⓘ
structural approach over computational examples ⓘ |
| field |
algebraic number theory
ⓘ
number theory ⓘ |
| focusesOn | conceptual foundations of algebraic number theory ⓘ |
| hasReputation |
classical reference in algebraic number theory
ⓘ
difficult ⓘ |
| hasStructure | systematic development from local to global theory ⓘ |
| hasTopic |
Chebotarev density theorem
ⓘ
surface form:
Chebotarev density theorem (contextual)
Galois theory of global fields ⓘ Galois theory of local fields ⓘ Haar measure on local fields ⓘ L-functions ⓘ Poisson summation formula ⓘ Tate’s thesis framework ⓘ adeles ⓘ characters of local fields ⓘ class field theory ⓘ discriminants ⓘ global fields ⓘ ideles ⓘ local fields ⓘ norms in number fields ⓘ ramification theory ⓘ trace in number fields ⓘ valuation theory ⓘ valuations ⓘ zeta functions ⓘ |
| influenced | modern expositions of algebraic number theory ⓘ |
| language | English ⓘ |
| level | graduate ⓘ |
| partOf | 20th-century mathematical literature ⓘ |
| publicationYear | 1967 ⓘ |
| publisher | Springer ⓘ |
| series | Die Grundlehren der mathematischen Wissenschaften ⓘ |
| style |
abstract
ⓘ
rigorous ⓘ |
| targetAudience |
graduate students in mathematics
ⓘ
research mathematicians in number theory ⓘ |
| usedAs | graduate textbook in mathematics ⓘ |
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: Basic Number Theory Description of subject: Basic Number Theory is a foundational graduate-level text by André Weil that systematically develops algebraic number theory and related concepts with exceptional rigor and depth.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
André Weil