Bombieri norm
E571013
The Bombieri norm is a mathematical norm on polynomials, introduced by Enrico Bombieri, that is particularly useful in analytic number theory and the study of polynomial inequalities.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Bombieri norm canonical | 1 |
| Bombieri scalar product | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6150018 — 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: Bombieri norm Context triple: [Enrico Bombieri, knownFor, Bombieri norm]
-
A.
Banach–Mazur distance
The Banach–Mazur distance is a numerical measure in functional analysis that quantifies how "far apart" two finite-dimensional normed vector spaces are up to linear isomorphism.
-
B.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
C.
Minkowski inequality
The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
-
D.
Bernstein inequalities
Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
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E.
Fefferman–Phong inequality
The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
- 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: Bombieri norm Target entity description: The Bombieri norm is a mathematical norm on polynomials, introduced by Enrico Bombieri, that is particularly useful in analytic number theory and the study of polynomial inequalities.
-
A.
Banach–Mazur distance
The Banach–Mazur distance is a numerical measure in functional analysis that quantifies how "far apart" two finite-dimensional normed vector spaces are up to linear isomorphism.
-
B.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
C.
Minkowski inequality
The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
-
D.
Bernstein inequalities
Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
-
E.
Fefferman–Phong inequality
The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
- F. None of above. chosen
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
concept in analytic number theory
ⓘ
mathematical norm ⓘ norm on polynomials ⓘ |
| appliesTo |
homogeneous polynomials
ⓘ
multivariate polynomials ⓘ |
| definedOn | vector space of homogeneous polynomials of fixed degree ⓘ |
| fieldOfUse |
Diophantine approximation
ⓘ
analytic number theory ⓘ arithmetic geometry ⓘ polynomial inequalities ⓘ |
| hasProperty |
compatible with the Bombieri scalar product
ⓘ
defines a Hilbert space structure on spaces of homogeneous polynomials ⓘ equivalent to certain coefficient-weighted ℓ2 norms ⓘ invariant under unitary changes of variables ⓘ rotation invariant under orthogonal changes of variables ⓘ |
| introducedBy | Enrico Bombieri ⓘ |
| isToolIn |
analytic estimates for exponential sums involving polynomials
ⓘ
proofs of polynomial inequalities ⓘ |
| namedAfter | Enrico Bombieri ⓘ |
| relatedTo |
Bombieri scalar product
ⓘ
linked to:
Bombieri norm
Hilbert space of homogeneous polynomials ⓘ L2 norm on the unit sphere via integral representations ⓘ |
| satisfies |
homogeneity
ⓘ
positive definiteness ⓘ triangle inequality ⓘ |
| usedFor |
bounding values of polynomials on the unit sphere
ⓘ
estimating sizes of polynomial coefficients ⓘ height estimates in Diophantine problems ⓘ inequalities relating sup norms and coefficient norms ⓘ studying distribution of zeros of polynomials ⓘ |
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: Bombieri norm Description of subject: The Bombieri norm is a mathematical norm on polynomials, introduced by Enrico Bombieri, that is particularly useful in analytic number theory and the study of polynomial inequalities.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Bombieri norm