Dutch school of number theory
E824094
The Dutch school of number theory is a mathematical tradition centered in the Netherlands, known for its influential contributions to Diophantine approximation, uniform distribution, and analytic number theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Dutch school of number theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9838944 — 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: Dutch school of number theory Context triple: [Johan Frederik Koksma, areaOfInfluence, Dutch school of number theory]
-
A.
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.
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B.
Hardy–Littlewood circle method
The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
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C.
Iwasawa theory
Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
-
D.
Polish School of Mathematics
The Polish School of Mathematics was a renowned early 20th-century mathematical tradition centered in cities like Warsaw and Lwów, noted for its groundbreaking work in areas such as functional analysis, topology, and logic.
-
E.
Lwów School of Mathematics
The Lwów School of Mathematics was a renowned early 20th-century Polish mathematical community centered in Lwów, famous for its groundbreaking work in functional analysis, set theory, and probability, and for its collaborative problem-solving culture documented in the Scottish Book.
- 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: Dutch school of number theory Target entity description: The Dutch school of number theory is a mathematical tradition centered in the Netherlands, known for its influential contributions to Diophantine approximation, uniform distribution, and analytic number theory.
-
A.
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.
-
B.
Hardy–Littlewood circle method
The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
-
C.
Iwasawa theory
Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
-
D.
Polish School of Mathematics
The Polish School of Mathematics was a renowned early 20th-century mathematical tradition centered in cities like Warsaw and Lwów, noted for its groundbreaking work in areas such as functional analysis, topology, and logic.
-
E.
Lwów School of Mathematics
The Lwów School of Mathematics was a renowned early 20th-century Polish mathematical community centered in Lwów, famous for its groundbreaking work in functional analysis, set theory, and probability, and for its collaborative problem-solving culture documented in the Scottish Book.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf | mathematical tradition ⓘ |
| associatedWithInstitution |
Eindhoven University of Technology
NERFINISHED
ⓘ
Leiden University NERFINISHED ⓘ Radboud University Nijmegen NERFINISHED ⓘ University of Amsterdam NERFINISHED ⓘ University of Groningen NERFINISHED ⓘ |
| collaboratesWith |
British school of number theory
NERFINISHED
ⓘ
French school of number theory ⓘ German school of number theory ⓘ |
| contributedTo |
applications of analytic methods in Diophantine problems
ⓘ
development of discrepancy theory ⓘ development of uniform distribution modulo 1 ⓘ |
| country | Netherlands ⓘ |
| field | number theory ⓘ |
| focusesOn |
Diophantine approximation
ⓘ
analytic number theory ⓘ uniform distribution theory ⓘ |
| hasLanguage |
Dutch
ⓘ
English ⓘ |
| hasMethodologicalEmphasis |
analytic techniques
ⓘ
geometric methods in number theory ⓘ probabilistic techniques ⓘ |
| hasNotableResearcher |
C. J. Mozzochi
NERFINISHED
ⓘ
H. Halberstam NERFINISHED ⓘ J. F. Koksma NERFINISHED ⓘ J. H. van Lint NERFINISHED ⓘ J. W. S. Cassels NERFINISHED ⓘ M. J. B. van der Poorten NERFINISHED ⓘ N. G. de Bruijn NERFINISHED ⓘ P. Erdős NERFINISHED ⓘ R. Tijdeman NERFINISHED ⓘ |
| influencedBy |
A. Schinzel
NERFINISHED
ⓘ
H. Halberstam NERFINISHED ⓘ J. F. Koksma NERFINISHED ⓘ J. H. van Lint NERFINISHED ⓘ N. G. de Bruijn NERFINISHED ⓘ R. Tijdeman NERFINISHED ⓘ |
| knownFor |
Diophantine equations
ⓘ
additive number theory ⓘ discrepancy theory ⓘ distribution of prime numbers ⓘ exponential sums ⓘ metric Diophantine approximation ⓘ probabilistic methods in number theory ⓘ sieve methods ⓘ uniform distribution modulo 1 ⓘ |
| partOf | European school of number theory NERFINISHED ⓘ |
| timePeriod |
20th century
ⓘ
21st century ⓘ |
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: Dutch school of number theory Description of subject: The Dutch school of number theory is a mathematical tradition centered in the Netherlands, known for its influential contributions to Diophantine approximation, uniform distribution, and analytic number theory.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.