An Introduction to Sieve Methods and Their Applications 1st Edition by Alina Carmen Cojocaru, Ram Murty 9780511131493 0511131496

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Product details:

ISBN 10: 0511131496

ISBN 13: 9780511131493

Author: Alina Carmen Cojocaru; M. Ram Murty

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.

Table of contents:

Chapter 1: Some basic notions
Chapter 2: Some elementary sieves
Chapter 3: The normal order method
Chapter 4: The Turán sieve
Chapter 5: The sieve of Eratosthenes
Chapter 6: Brun’s sieve
Chapter 7: Selberg’s sieve
Chapter 8: The large sieve
Chapter 9: The Bombieri–Vinogradov theorem
Chapter 10: The lower bound sieve
Chapter 11: New directions in sieve theory

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Tags: Alina Carmen Cojocaru, Ram Murty, Introduction, Sieve