Halász theorem

E637298

theorem in analytic number theory

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.

Try in SPARQL Jump to: Surface forms Disambiguation Statements Elicitation Referenced by

All labels observed (3)

Label	Occurrences
Halász method	1
Halász theorem canonical	1
Halász’s theorem	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 ⓘ
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 ⓘ
provedBy	Gábor Halász ⓘ
provides	sharp bounds on mean values of multiplicative functions ⓘ
relatedTo	Delange theorem ⓘ linked to: Erdős–Wintner theorem Dirichlet characters modulo q ⓘ linked to: Dirichlet characters Erdős–Wintner theorem ⓘ Granville–Soundararajan theory of pretentious multiplicative functions ⓘ 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 ⓘ Fourier analysis on the unit circle ⓘ Halász–Montgomery inequality ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Multiplicative Number Theory → hasClassicResult → Halász theorem ⓘ

Selberg–Delange method results → relatedTo → Halász’s theorem ⓘ

linked to: Halász theorem

Turán's method → relatedTo → Halász method ⓘ