A Course in Arithmetic
E253120
A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
All labels observed (3)
| Label | Occurrences |
|---|---|
| A Course in Arithmetic canonical | 1 |
| Cours d’arithmétique | 1 |
| Serre, A Course in Arithmetic | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2306399 — 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: A Course in Arithmetic Context triple: [Jean-Pierre Serre, notableWork, A Course in Arithmetic]
-
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.
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.
-
C.
Number Theory: An Approach through History from Hammurapi to Legendre
"Number Theory: An Approach through History from Hammurapi to Legendre" is a historical and expository book by André Weil that traces the development of number theory from ancient Mesopotamia to the early 19th century.
-
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.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
- 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: A Course in Arithmetic Target entity description: A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
-
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.
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.
-
C.
Number Theory: An Approach through History from Hammurapi to Legendre
"Number Theory: An Approach through History from Hammurapi to Legendre" is a historical and expository book by André Weil that traces the development of number theory from ancient Mesopotamia to the early 19th century.
-
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.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics textbook ⓘ |
| author | Jean-Pierre Serre ⓘ |
| classification |
algebraic number theory text
ⓘ
analytic number theory text ⓘ |
| contains | exercises ⓘ |
| containsChapterOn |
Galois representations (introductory)
ⓘ
modular forms and modular curves ⓘ p-adic analysis ⓘ zeta and L-functions ⓘ |
| countryOfOrigin | France ⓘ |
| field |
algebra
ⓘ
arithmetic ⓘ number theory ⓘ |
| hasAuthorNobelEquivalent |
Jean-Pierre Serre
ⓘ
surface form:
Jean-Pierre Serre is a Fields Medalist
|
| hasFormat |
ebook
ⓘ
hardcover ⓘ softcover ⓘ |
| hasReputation | classic text in number theory ⓘ |
| influenced | modern expositions of algebraic number theory ⓘ |
| isbnExample | 978-0-387-90420-0 ⓘ |
| language | French ⓘ |
| level |
advanced undergraduate
ⓘ
graduate ⓘ |
| notableFor |
concise exposition
ⓘ
elegant treatment of fundamental arithmetic concepts ⓘ |
| originalPublicationYear | 1970 ⓘ |
| originalTitle |
A Course in Arithmetic
self-linksurface differs
ⓘ
surface form:
Cours d’arithmétique
|
| pageCountApproximate | 200 ⓘ |
| publicationYear | 1973 ⓘ |
| publisher | Springer ⓘ |
| series | Graduate Texts in Mathematics ⓘ |
| subject |
Dirichlet characters
ⓘ
class field theory (introductory) ⓘ l-adic representations (introductory) ⓘ modular forms ⓘ p-adic numbers ⓘ zeta functions ⓘ |
| targetAudience |
mathematics students
ⓘ
research mathematicians (as reference) ⓘ |
| usedAs | standard reference in number theory courses ⓘ |
| volumeInSeries | 7 ⓘ |
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: A Course in Arithmetic Description of subject: A Course in Arithmetic is a classic introductory text in number theory by Jean-Pierre Serre, renowned for its concise and elegant treatment of fundamental arithmetic and algebraic concepts.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Serre, A Course in Arithmetic
this entity surface form:
Cours d’arithmétique