Large sieve

The large sieve is a method (or family of methods and related ideas) in analytic number theory.

Its name comes from its original application: given a set $S \subset \{ 1,\ldots,N \}$ such that the elements of S are forbidden to lie in a set A_p ⊂ Z/p Z modulo every prime p, how large can S be? Here A_p is thought of as being large, i.e., at least as large as a constant times p; if this is not the case, we speak of a small sieve. (The term "sieve" is seen as alluding to, say, sifting ore for gold: we "sift out" the integers falling in one of the forbidden congruence classes modulo p, and ask ourselves how much is left at the end.)

单词	Large sieve
释义	Large sieve 原声例句圣诞吃什么 Then you're gonna take a large sieve and put it over a four cup Pyrex pitcher. 然后你要拿一个大筛子，把它放在一个四杯的 Pyrex 水罐上。英语百科 Large sieve The large sieve is a method (or family of methods and related ideas) in analytic number theory. Its name comes from its original application: given a set $S \subset \{ 1,\ldots,N \}$ such that the elements of S are forbidden to lie in a set A_p ⊂ Z/p Z modulo every prime p, how large can S be? Here A_p is thought of as being large, i.e., at least as large as a constant times p; if this is not the case, we speak of a small sieve. (The term "sieve" is seen as alluding to, say, sifting ore for gold: we "sift out" the integers falling in one of the forbidden congruence classes modulo p, and ask ourselves how much is left at the end.)
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