van der Corput lemma

E776133

mathematical lemma result in harmonic analysis

The van der Corput lemma is a fundamental result in analytic number theory and harmonic analysis that provides bounds for oscillatory integrals and exponential sums, crucial for estimating error terms in various asymptotic formulas.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (1)

Surface form	Occurrences
van der Corput lemma in harmonic analysis	1

Statements (45)

Predicate	Object
instanceOf	mathematical lemma ⓘ result in harmonic analysis ⓘ
appearsIn	monographs on exponential sums ⓘ texts on analytic number theory ⓘ texts on harmonic analysis ⓘ
appliesTo	exponential sums ⓘ oscillatory integrals ⓘ trigonometric integrals ⓘ
assumes	nonvanishing derivative or curvature conditions ⓘ smoothness conditions on the phase function ⓘ
field	analytic number theory ⓘ harmonic analysis ⓘ
hasFormulation	discrete exponential sum version ⓘ higher-derivative version for oscillatory integrals ⓘ one-dimensional oscillatory integral estimate ⓘ
hasVersion	van der Corput A-process NERFINISHED ⓘ van der Corput B-process NERFINISHED ⓘ
implies	cancellation in exponential sums ⓘ decay of oscillatory integrals under derivative conditions ⓘ
influenced	development of modern exponential sum techniques ⓘ methods for bounding oscillatory integrals in analysis ⓘ
namedAfter	J. G. van der Corput NERFINISHED ⓘ
provides	bounds for exponential sums ⓘ bounds for oscillatory integrals ⓘ
relatedTo	Weyl differencing NERFINISHED ⓘ Weyl’s inequality NERFINISHED ⓘ equidistribution modulo 1 ⓘ method of exponential sums ⓘ stationary phase method ⓘ van der Corput inequality NERFINISHED ⓘ
timePeriod	20th century mathematics ⓘ
typicalConclusion	integral bounded by constant times lambda to a negative power ⓘ
typicalHypothesis	k-th derivative of phase bounded away from zero ⓘ
usedFor	bounding Weyl sums ⓘ bounding exponential sums over integers ⓘ bounding oscillatory integrals with phase functions ⓘ bounding trigonometric sums ⓘ estimating error terms in asymptotic formulas ⓘ proving equidistribution results ⓘ proving estimates in the circle method ⓘ
usedIn	Fourier analysis on the real line ⓘ discrepancy theory ⓘ estimates for exponential integrals in PDE ⓘ metric number theory ⓘ proofs of bounds for the Riemann zeta function ⓘ

Referenced by (2)

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

Johannes G. van der Corput → knownFor → van der Corput lemma ⓘ

Johannes G. van der Corput → notableConcept → van der Corput lemma ⓘ

this entity surface form: van der Corput lemma in harmonic analysis