Bohr–Courant theorem
E904000
The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Bohr–Courant theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11085785 — 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: Bohr–Courant theorem Context triple: [Voronin universality theorem, relatedTo, Bohr–Courant theorem]
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A.
Courant–Fischer min–max theorem
The Courant–Fischer min–max theorem is a fundamental result in linear algebra and spectral theory that characterizes the eigenvalues of a Hermitian (or symmetric) matrix via variational min–max principles over subspaces.
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B.
Bose–Nair theorem
The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
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C.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
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D.
Paley–Wiener theorem
The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
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E.
Bernstein theorem
Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
- 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: Bohr–Courant theorem Target entity description: The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
-
A.
Courant–Fischer min–max theorem
The Courant–Fischer min–max theorem is a fundamental result in linear algebra and spectral theory that characterizes the eigenvalues of a Hermitian (or symmetric) matrix via variational min–max principles over subspaces.
-
B.
Bose–Nair theorem
The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
-
C.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
D.
Paley–Wiener theorem
The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
-
E.
Bernstein theorem
Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
- F. None of above. chosen
Statements (28)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
theorem in analytic number theory ⓘ |
| appliesTo |
Dirichlet series
NERFINISHED
ⓘ
Riemann zeta function NERFINISHED ⓘ |
| concerns |
distribution of values of the Riemann zeta function
ⓘ
values taken by Dirichlet series in the complex plane ⓘ |
| describes |
value distribution of Dirichlet series
ⓘ
value distribution of the Riemann zeta function ⓘ |
| era | early 20th century mathematics ⓘ |
| field |
analytic number theory
ⓘ
complex analysis ⓘ |
| hasAuthor |
Harald Bohr
NERFINISHED
ⓘ
Richard Courant NERFINISHED ⓘ |
| historicalRole |
early result on value distribution of zeta and L-functions
ⓘ
precursor to modern universality results in analytic number theory ⓘ |
| isPrecursorOf |
Voronin universality theorem
NERFINISHED
ⓘ
universality theorems for the Riemann zeta function ⓘ |
| isRelatedTo |
Bohr–Jessen theory
NERFINISHED
ⓘ
Bohr’s work on almost periodic functions ⓘ universality theorems ⓘ value-distribution of holomorphic functions ⓘ |
| namedAfter |
Harald Bohr
NERFINISHED
ⓘ
Richard Courant NERFINISHED ⓘ |
| topic |
Dirichlet series
ⓘ
Riemann zeta function NERFINISHED ⓘ value-distribution theory of zeta-functions ⓘ |
| usedIn |
research on universality of zeta and L-functions
ⓘ
studies of complex zeros and values of Dirichlet series ⓘ |
How these facts were elicited
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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: Bohr–Courant theorem Description of subject: The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.