An Introduction to Sieve Methods and Their Applications (London Mathematical Society Student Texts, Series Number 66)

Sieve Theory Has A Rich And Romantic History. The Ancient Question Of Whether There Exist Infinitely Many Twin Primes (primes P Such That P+2 Is Also Prime), And Goldbach's Conjecture That Every Even Number Can Be Written As The Sum Of Two Prime Numbers, Have Been Two Of The Problems That Have Inspired The Development Of The Theory. This Book Provides A Motivated Introduction To Sieve Theory. Rather Than Focus On Technical Details Which Can Obscure The Beauty Of The Theory, The Authors Focus On Examples And Applications, Developing The Theory In Parallel. The Text Can Be Used For A Senior Level Undergraduate Course Or An Introductory Graduate Course In Analytic Number Theory, And Non-experts Can Gain A Quick Introduction To The Techniques Of The Subject. 1. Some Basic Notions -- 2. Some Elementary Sieves -- 3. Normal Order Method -- 4. Turan Sieve -- 5. Sieve Of Eratosthenes -- 6. Brun's Sieve -- 7. Selberg's Sieve -- 8. Large Sieve -- 9. Bombieri -- Vinogradov Theorem -- 10. Lower Bound Sieve -- 11. New Directions In Sieve Theory. Alina Carmen Cojocaru, M. Ram Murty. Includes Bibliographical References (p. 218-221) And Index. Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers, have been two of the problems that have inspired the development of the theory.This book provides a motivated introduction to sieve theory. Rather than focus on technical details, which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or for an introductory graduate course in analytic number theory, and non-experts can gain a quick introduction to the techniques of the subject.

Sieve theory has a rich and romantic history. The ancient question of whether there exist infinitely many twin primes (primes p such that p+2 is also prime), and Goldbach's conjecture that every even number can be written as the sum of two prime numbers, have been two of the problems that have inspired the development of the theory. This book provides a motivating introduction to sieve theory. Rather than focus on technical details which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or an introductory graduate course in analytic number theory.

"This book provides a motivated introduction to sieve theory. Rather than focus on technical details, which can obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. The text can be used for a senior level undergraduate course or for an introductory graduate course in analytic number theory, and non-experts can gain a quick introduction to the techniques of the subject."--BOOK JACKET This book provides a motivated introduction to sieve theory. Rather than focus on technical details which obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. Suitable for a senior level undergraduate course or an introductory graduate course in analytic number theory Rather than focus on the technical details which can obscure the beauty of sieve theory, the authors focus on examples and applications, developing the theory in parallel A. F. Mobius (1790-1868) introduced the famous Mobius function (.) in 1831 and proved the now well-known inversion formula.