The Riemann Hypothesis And Prime Number Theorem

The Riemann Hypothesis and Prime Number Theorem

The Riemann Hypothesis

This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the “expert witnesses” whose insight into this field is both invaluable and irreplaceable.

The Prime Number Theorem

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.