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Definition: Sieve, Sieve Problem

A sieve is a tuple $(\mathcal A_N,\mathcal P_\rho,\mathcal R)$ consisting of

Given a sieve, a sieve problem is the problem of estimating the cardinality of all elements of $\mathcal A$ that are not congruent to any of the residue classes in $\mathcal R$, i.e. the number $$S(N):=|\{n\in\mathbb N\mid a_n\not\in R\}|.$$

| | | | | created: 2020-05-17 11:58:07 | modified: 2020-05-17 12:18:33 | by: bookofproofs | references: [8526], [8527]

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Bibliography (further reading)

[8526] Halberstam, H; Roth, K.F.: “Sequences”, Oxford at the Claredon Press, 1966

[8527] Schwarz, Wolfgang: “Einf├╝hrung in Siebmethoden der analytischen Zahlentheorie”, B.I.-Wissenschaftsverlag, 1974