Turán's method
E750084
Turán's method is a powerful technique in analytic and probabilistic number theory that uses inequalities for power sums of sequences to derive bounds for arithmetic functions and related quantities.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Turán's method canonical | 2 |
| Turán power sum method | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8669826 — 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: Turán's method Context triple: [Pál Turán, knownFor, Turán's method]
-
A.
Erdős–Stone theorem
The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
-
B.
Erdős on Graphs: His Legacy
Erdős on Graphs: His Legacy is a mathematical monograph by Fan Chung and Ronald Graham that surveys and extends Paul Erdős’s influential work in graph theory and combinatorics.
-
C.
Hardy–Littlewood circle method
The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
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D.
Erdős–Ko–Rado theorem
The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
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E.
Erdős–Gallai theorem
The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
- 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: Turán's method Target entity description: Turán's method is a powerful technique in analytic and probabilistic number theory that uses inequalities for power sums of sequences to derive bounds for arithmetic functions and related quantities.
-
A.
Erdős–Stone theorem
The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
-
B.
Erdős on Graphs: His Legacy
Erdős on Graphs: His Legacy is a mathematical monograph by Fan Chung and Ronald Graham that surveys and extends Paul Erdős’s influential work in graph theory and combinatorics.
-
C.
Hardy–Littlewood circle method
The Hardy–Littlewood circle method is a powerful analytic number theory technique that uses complex analysis and Fourier series to study additive problems such as Waring’s problem and the Goldbach conjecture.
-
D.
Erdős–Ko–Rado theorem
The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
-
E.
Erdős–Gallai theorem
The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
- F. None of above. chosen
Statements (38)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical method
ⓘ
technique in analytic number theory ⓘ technique in probabilistic number theory ⓘ |
| appliesTo |
Dirichlet series
ⓘ
L-functions ⓘ arithmetic functions ⓘ |
| areaOfApplication |
additive number theory
ⓘ
multiplicative number theory ⓘ prime number theory ⓘ |
| basedOn |
mean value estimates
ⓘ
power sum inequalities ⓘ |
| characteristicFeature |
conversion of mean value bounds into pointwise bounds
ⓘ
use of high-order power sums ⓘ |
| developedBy | Pál Turán ⓘ |
| field |
analytic number theory
ⓘ
number theory ⓘ probabilistic number theory ⓘ |
| goal |
derive bounds for arithmetic functions
ⓘ
obtain lower bounds ⓘ obtain upper bounds ⓘ |
| hasAlternativeName |
Turán power sum method
ⓘ
linked to:
Turán's method
|
| historicalPeriod | 20th-century mathematics ⓘ |
| influenced | later methods in analytic number theory ⓘ |
| involves |
Cauchy–Schwarz inequality
ⓘ
Hölder inequality ⓘ moments of sequences ⓘ power moments of arithmetic functions ⓘ |
| namedAfter | Pál Turán ⓘ |
| relatedTo |
Halász method
ⓘ
linked to:
Halász theorem
large sieve method ⓘ probabilistic methods in number theory ⓘ |
| usedFor |
bounds on character sums
ⓘ
distribution of values of arithmetic functions ⓘ estimates for multiplicative functions ⓘ probabilistic models of zeta and L-functions ⓘ zero-free regions for L-functions ⓘ |
| uses |
estimates for power sums of sequences
ⓘ
inequalities for power sums ⓘ |
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: Turán's method Description of subject: Turán's method is a powerful technique in analytic and probabilistic number theory that uses inequalities for power sums of sequences to derive bounds for arithmetic functions and related quantities.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Turán's method