van der Corput method

E776134

analytic number theory technique method for estimating exponential sums

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.

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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 ⓘ

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