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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Brun sieve ： ウィキペディア英語版 Brun sieve In the field of number theory, the Brun sieve (also called Brun's pure sieve) is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by Viggo Brun in 1915. ==Description== In terms of sieve theory the Brun sieve is of ''combinatorial type''; that is, it derives from a careful use of the inclusion-exclusion principle. Let ''A'' be a set of positive integers ≤ ''x'' and let ''P'' be a set of primes. For each ''p'' in ''P'', let ''A''''p'' denote the set of elements of ''A'' divisible by ''p'' and extend this to let ''A''''d'' the intersection of the ''A''''p'' for ''p'' dividing ''d'', when ''d'' is a product of distinct primes from ''P''. Further let A1 denote ''A'' itself. Let ''z'' be a positive real number and ''P''(''z'') denote the primes in ''P'' ≤ ''z''. The object of the sieve is to estimate :$S(A,P,z)\; =\; \backslash left\backslash vert\; A\; \backslash setminus\; \backslash bigcup\_\; A\_p\; \backslash right\backslash vert\; .$ We assume that |''A''''d''| may be estimated by :$\backslash left\backslash vert\; A\_d\; \backslash right\backslash vert\; =\; \backslash frac\; X\; +\; R\_d$ where ''w'' is a multiplicative function and ''X''   =   |''A''|. Let :$W(z)\; =\; \backslash prod\_\; \backslash left(1\; -\; \backslash frac\; \backslash right)\; .$ 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「Brun sieve」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.