van der Corput method
E776134
The van der Corput method is a technique in analytic number theory used to estimate exponential sums and derive bounds for problems such as the distribution of prime numbers and lattice point counting.
All labels observed (1)
| Label | Occurrences |
|---|---|
| van der Corput method canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9070945 — 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: van der Corput method Context triple: [Johannes G. van der Corput, knownFor, van der Corput method]
-
A.
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.
-
B.
Dirichlet hyperbola method
The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
-
C.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
-
D.
Chebyshev functions
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
-
E.
Bombieri–Vinogradov theorem
The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
- 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: van der Corput method Target entity description: The van der Corput method is a technique in analytic number theory used to estimate exponential sums and derive bounds for problems such as the distribution of prime numbers and lattice point counting.
-
A.
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.
-
B.
Dirichlet hyperbola method
The Dirichlet hyperbola method is a technique in analytic number theory used to estimate sums of arithmetic functions by splitting double sums along a hyperbola to obtain asymptotic formulas.
-
C.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
-
D.
Chebyshev functions
Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
-
E.
Bombieri–Vinogradov theorem
The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
analytic number theory technique
ⓘ
method for estimating exponential sums ⓘ |
| appliesTo |
Weyl sums of the form ∑ e(P(n))
ⓘ
exponential sums of the form ∑ e(f(n)) ⓘ |
| basedOn |
Cauchy–Schwarz inequality
NERFINISHED
ⓘ
differencing of exponential sums ⓘ partial summation ⓘ |
| developedInField | early 20th century analytic number theory ⓘ |
| field | analytic number theory ⓘ |
| goal |
obtain nontrivial cancellation in exponential sums
ⓘ
reduce degree of the phase polynomial in exponential sums ⓘ |
| hasVariant |
van der Corput A-process
NERFINISHED
ⓘ
van der Corput B-process NERFINISHED ⓘ van der Corput differencing method NERFINISHED ⓘ van der Corput inequality NERFINISHED ⓘ |
| improves | trivial bounds for exponential sums ⓘ |
| influenced | modern methods in exponential sum estimates ⓘ |
| namedAfter | J. G. van der Corput NERFINISHED ⓘ |
| relatedConcept |
van der Corput differencing lemma
NERFINISHED
ⓘ
van der Corput inequality for sequences ⓘ |
| relatedTo |
Hardy–Littlewood circle method
NERFINISHED
ⓘ
Vinogradov’s method NERFINISHED ⓘ Weyl differencing ⓘ Weyl’s method NERFINISHED ⓘ van der Corput lemma on oscillatory integrals NERFINISHED ⓘ |
| requires | smoothness conditions on the phase ⓘ |
| typicalInput | phase function with several derivatives ⓘ |
| usedBy |
analytic combinatorialists
ⓘ
mathematical analysts ⓘ number theorists ⓘ |
| usedFor |
Weyl sums estimation
ⓘ
bounding error terms in asymptotic formulas ⓘ bounding exponential sums ⓘ bounding exponential sums over integers ⓘ bounding exponential sums over polynomial phases ⓘ bounding exponential sums over primes ⓘ estimating exponential sums ⓘ lattice point counting problems ⓘ proving equidistribution results ⓘ studying distribution of prime numbers ⓘ trigonometric sums estimation ⓘ |
| usedIn |
bounds for exponential sums in prime number theory
ⓘ
discrepancy theory ⓘ estimates for the Riemann zeta function ⓘ proofs of bounds for the circle problem ⓘ proofs of bounds for the divisor problem ⓘ uniform distribution modulo 1 ⓘ |
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: van der Corput method Description of subject: The van der Corput method is a technique in analytic number theory used to estimate exponential sums and derive bounds for problems such as the distribution of prime numbers and lattice point counting.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.