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In number theory, the fundamental lemma of sieve theory is any of several results that systematize the process of applying sieve methods to particular problems. Halberstam & Richert 〔 〕 write: Diamond & Halberstam〔 〕 attribute the terminology ''Fundamental Lemma'' to Jonas Kubilius. ==Common notation== We use these notations: * ''A'' is a set of ''X'' positive integers, and ''A''''d'' is its subset of integers divisible by ''d'' * ''w''(''d'') and ''R''''d'' are functions of ''A'' and of ''d'' that estimate the number of elements of ''A'' that are divisible by ''d'', according to the formula : :Thus ''w''(''d'') / ''d'' represents an approximate density of members divisible by ''d'', and ''R''''d'' represents an error or remainder term. * ''P'' is a set of primes, and ''P''(''z'') is the product of those primes ≤ ''z'' * ''S''(''A'', ''P'', ''z'') is the number of elements of ''A'' not divisible by any prime in ''P'' that is ≤ ''z'' * κ is a constant, called the sifting density,〔 that appears in the assumptions below. It is a weighted average of the number of residue classes sieved out by each prime. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「fundamental lemma of sieve theory」の詳細全文を読む スポンサード リンク
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