Halász theorem
E637298
Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Halász theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7030752 — 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: Halász theorem Context triple: [Multiplicative Number Theory, hasClassicResult, Halász theorem]
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
C.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
D.
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.
-
E.
Steinhaus theorem
The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
- 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: Halász theorem Target entity description: Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
C.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
D.
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.
-
E.
Steinhaus theorem
The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf | theorem in analytic number theory ⓘ |
| appearsIn | research on mean values of arithmetic functions ⓘ |
| appliesTo |
bounded multiplicative functions
ⓘ
complex-valued multiplicative functions ⓘ |
| assumes |
growth conditions on the multiplicative function
ⓘ
multiplicativity of the function ⓘ |
| characterizes |
distance of a multiplicative function from characters or n^{it}
ⓘ
when a multiplicative function has large mean value ⓘ |
| concerns |
average behavior of multiplicative functions
ⓘ
partial sums of multiplicative functions over n ≤ x ⓘ |
| context |
distribution of additive arithmetic functions via multiplicative methods
ⓘ
probabilistic number theory ⓘ |
| field |
analytic number theory
ⓘ
number theory ⓘ |
| hasConsequence |
logarithmic density results for multiplicative functions
ⓘ
mean value estimates uniform in the range of summation ⓘ |
| hasVariant | Halász inequality for multiplicative functions NERFINISHED ⓘ |
| implies |
bounds for partial sums of multiplicative functions
ⓘ
cancellation in sums of non-pretentious multiplicative functions ⓘ |
| influenced |
modern theory of multiplicative functions
ⓘ
pretentious analytic number theory ⓘ |
| mainTopic |
mean values of multiplicative functions
ⓘ
multiplicative functions ⓘ |
| mathematicalDomain | additive and multiplicative number theory ⓘ |
| namedAfter | Gábor Halász NERFINISHED ⓘ |
| provedBy | Gábor Halász NERFINISHED ⓘ |
| provides | sharp bounds on mean values of multiplicative functions ⓘ |
| relatedTo |
Delange theorem
NERFINISHED
ⓘ
Dirichlet characters modulo q NERFINISHED ⓘ Erdős–Wintner theorem NERFINISHED ⓘ Granville–Soundararajan theory of pretentious multiplicative functions NERFINISHED ⓘ large sieve methods ⓘ mean values over initial intervals of the integers ⓘ pretentious approach to multiplicative functions ⓘ |
| timePeriod | 20th century mathematics ⓘ |
| typeOfBound | asymptotically sharp ⓘ |
| typicalForm | upper bound for |∑_{n≤x} f(n)| in terms of a distance parameter ⓘ |
| usedFor |
bounding correlations of multiplicative functions
ⓘ
estimating mean values of Dirichlet characters ⓘ estimating mean values of the Liouville function ⓘ estimating mean values of the Möbius function ⓘ proving results on sign changes of multiplicative functions ⓘ studying distribution of values of multiplicative functions ⓘ |
| usesConcept |
Dirichlet series
NERFINISHED
ⓘ
Fourier analysis on the unit circle ⓘ Halász–Montgomery inequality NERFINISHED ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Halász theorem Description of subject: Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.