In mathematics, 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 such that the elements of S are forbidden to lie in a set Ap ⊂ Z/p Z modulo every prime p, how large can S be? Here Ap 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.)
Read more about Large Sieve: Development, History
Famous quotes containing the words large and/or sieve:
“O thou undaunted daughter of desires!
By all thy dower of lights and fires;
By all the eagle in thee, all the dove;
By all thy lives and deaths of love;
By thy large draughts of intellectual day,
And by thy thirsts of love more large then they;
By all thy brim-fill’d Bowls of fierce desire,
By thy last Morning’s draught of liquid fire;
By the full kingdom of that final kiss
That seiz’d thy parting Soul, and seal’d thee his;”
—Richard Crashaw (1613?–1649)
“It’s like pushing marbles through a sieve. It means the sieve will never be the same again.”
—Before the 1972 Democratic Convention in Miami. As quoted in Crazy Salad, ch. 6, by Nora Ephron (1972)