van der Corput method for estimating exponential sums

E776136

The van der Corput method for estimating exponential sums is a classical analytic number theory technique that provides bounds for oscillatory sums by exploiting differencing and smoothness properties of the phase function.

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Statements (45)

Predicate Object
instanceOf analytic number theory method ⓘ
technique for bounding exponential sums ⓘ
appearsIn classical texts on analytic number theory ⓘ
monographs on exponential sums ⓘ
appliesTo exponential sums ⓘ
oscillatory sums ⓘ
assumes non-degeneracy conditions on the phase ⓘ
basedOn van der Corput differencing ⓘ
canYield sub-square-root cancellation in favorable cases ⓘ
classification classical method in analytic number theory ⓘ
coreIdea gain powers of cancellation via differencing ⓘ
replace original sum by sums of finite differences ⓘ
field analytic number theory ⓘ
goal exploit cancellation in oscillatory sums ⓘ
obtain upper bounds for exponential sums ⓘ
hasVariant van der Corput A-process ⓘ
van der Corput B-process ⓘ
historicalPeriod early 20th century ⓘ
influenced methods in additive combinatorics ⓘ
modern exponential sum techniques ⓘ
mathematicalDomain harmonic analysis ⓘ
number theory ⓘ
namedAfter J. G. van der Corput ⓘ
relatedConcept van der Corput lemma in harmonic analysis ⓘ
relatedTo Hardy–Littlewood circle method ⓘ
Vinogradov’s method ⓘ
Weyl differencing ⓘ
linked to: Weyl’s method

Weyl sums ⓘ
Weyl’s inequality ⓘ
linked to: Weyl inequalities

stationary phase method ⓘ
requires control of derivatives of the phase ⓘ
smooth phase function ⓘ
toolFor bounding error terms in asymptotic formulas ⓘ
estimating exponential integrals via discretization ⓘ
proving equidistribution of polynomial sequences modulo 1 ⓘ
typicalApplication bounding polynomial exponential sums ⓘ
bounding trigonometric sums ⓘ
estimates for Weyl sums with polynomial phases ⓘ
usedIn bounds for exponential sums over integers ⓘ
bounds for exponential sums over primes ⓘ
discrepancy theory ⓘ
distribution of prime numbers ⓘ
equidistribution problems ⓘ
uses differencing ⓘ
smoothness properties of the phase function ⓘ

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Referenced by (10)

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

Johannes G. van der Corput → notableConcept → van der Corput method for estimating exponential sums ⓘ
Vinogradov's three-primes theorem → usesConcept → Weyl differencing ⓘ
linked to: van der Corput method for estimating exponential sums
van der Corput lemma → relatedTo → Weyl differencing ⓘ
linked to: van der Corput method for estimating exponential sums
van der Corput method → hasVariant → van der Corput differencing method ⓘ
linked to: van der Corput method for estimating exponential sums
van der Corput method → relatedTo → Vinogradov’s method ⓘ
linked to: van der Corput method for estimating exponential sums
van der Corput inequality → isPartOf → van der Corput method for exponential sums ⓘ
linked to: van der Corput method for estimating exponential sums
van der Corput method for estimating exponential sums → relatedTo → Weyl sums ⓘ
linked to: van der Corput method for estimating exponential sums
van der Corput method for estimating exponential sums → hasVariant → van der Corput A-process ⓘ
linked to: van der Corput method for estimating exponential sums
van der Corput method for estimating exponential sums → hasVariant → van der Corput B-process ⓘ
linked to: van der Corput method for estimating exponential sums
theory of uniform distribution modulo 1 → studies → Weyl sums ⓘ
linked to: van der Corput method for estimating exponential sums