Turán's method

E750084

mathematical method technique in analytic number theory technique in probabilistic number theory

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.

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Statements (38)

Predicate	Object
instanceOf	mathematical method ⓘ technique in analytic number theory ⓘ technique in probabilistic number theory ⓘ
appliesTo	Dirichlet series ⓘ L-functions NERFINISHED ⓘ 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 NERFINISHED ⓘ
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 NERFINISHED ⓘ
historicalPeriod	20th-century mathematics ⓘ
influenced	later methods in analytic number theory ⓘ
involves	Cauchy–Schwarz inequality NERFINISHED ⓘ Hölder inequality NERFINISHED ⓘ moments of sequences ⓘ power moments of arithmetic functions ⓘ
namedAfter	Pál Turán NERFINISHED ⓘ
relatedTo	Halász method NERFINISHED ⓘ 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 ⓘ

Referenced by (2)

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

Pál Turán → knownFor → Turán's method ⓘ

Pál Turán → hasMethodNamedAfter → Turán's method ⓘ