The Prime Number Theorem (London Mathematical Society Student Texts, Series Number 53)

At First Glance The Prime Numbers Appear To Be Distributed In A Very Irregular Way Amongst The Integers, But It Is Possible To Produce A Simple Formula That Tells Us (in An Approximate But Well Defined Sense) How Many Primes We Can Expect To Find That Are Less Than Any Integer We Might Choose. The Prime Number Theorem Tells Us What This Formula Is And It Is Indisputably One Of The Great Classical Theorems Of Mathematics. This Textbook Gives An Introduction To The Prime Number Theorem Suitable For Advanced Undergraduates And Beginning Graduate Students. The Author's Aim Is To Show The Reader How The Tools Of Analysis Can Be Used In Number Theory To Attack A 'real' Problem, And It Is Based On His Own Experiences Of Teaching This Material. G. J. O. Jameson. Title From Publisher's Bibliographic System (viewed On 01 Jun 2016). Mode Of Access: World Wide Web. "Counter At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells us (in an approximate but well defined sense) how many primes we can expect to find that are less than any integer we might choose. The prime number theorem tells us what this formula is and it is indisputably one of the the great classical theorems of mathematics. This textbook gives an introduction to the prime number theorem suitable for advanced undergraduates and beginning graduate students. The author's aim is to show the reader how the tools of analysis can be used in number theory to attack a 'real' problem, and it is based on his own experiences of teaching this material."--Publisher's description Cover......Page 1 Title: The Prime Number Theorem......Page 2 Contents......Page 7 preface......Page 9 1 Foundations......Page 13 2 Some important Dirichlet series and arithmetic functions......Page 68 3 The basic theorems......Page 110 4 Prime numbers in residue classes: Dirichlet's theorem......Page 159 5 Error estimates and the Riemann hypothesis......Page 190 6 An \"elementary\" proof of the prime number theorem......Page 218 Appendix A......Page 235 Appendix B......Page 237 Appendix C......Page 240 Appendix D......Page 242 Appendix E......Page 244 Appendix F......Page 246 Appendix G......Page 250 Appendix H......Page 252 Bibliography......Page 261 Index......Page 263 At first glance the prime numbers appear to be distributed in a very irregular way amongst the integers, but it is possible to produce a simple formula that tells (in an approximate but well-defined sense) how many primes can be found that are less than any integer. The prime number theorem tells what this formula is and it is indisputably one of the the great classical theorems of mathematics. This textbook introduces the prime number theorem and is suitable for advanced undergraduates and beginning graduate students. The author deftly shows how analytical tools can be used in number theory to attack a 'real' problem. The prime number theorem is indisputably one of the great classical theorems of mathematics. Suitable for advanced undergraduates and beginning graduates, this textbook demonstrates how the tools of analysis can be used in number theory to attack a famous problem In this chapter, we assemble a number of ideas and techniques that will eventually be fitted together to achieve our aim.

This textbook demonstrates how the tools of analysis can be used in number theory to attack a famous problem.