1. The large sieve
- Author
-
P. X. Gallagher
- Subjects
Combinatorics ,Mathematics::Number Theory ,General Mathematics ,Modulo ,010102 general mathematics ,Large sieve ,Sieve analysis ,010103 numerical & computational mathematics ,0101 mathematics ,Mathematical proof ,01 natural sciences ,Mathematics - Abstract
1. The purpose of this paper is to give simple proofs for some recent versions of Linnik's large sieve, and some applications.The first theme of the large sieve is that an arbitrary set of Z integers in an interval of length N must be well distributed among most of the residue classes modulo p, for most small primes p, unless Z is small compared with N. Following improvements on Linnik's original result [1] by Renyi [2] and by Roth [3], Bombieri [4] recently proved the following inequality: Denote by Z(a, p) the number of integers in the set which are congruent to a modulo p.
- Published
- 1967