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.
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 NERFINISHED ⓘ invariant under unitary changes of variables ⓘ rotation invariant under orthogonal changes of variables ⓘ |
| introducedBy | Enrico Bombieri NERFINISHED ⓘ |
| isToolIn |
analytic estimates for exponential sums involving polynomials
ⓘ
proofs of polynomial inequalities ⓘ |
| namedAfter | Enrico Bombieri NERFINISHED ⓘ |
| relatedTo |
Bombieri scalar product
NERFINISHED
ⓘ
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 ⓘ |
Referenced by (1)
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