Robert C. Vaughan - Böcker

Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises.

This long-anticipated work shares the aims of its celebrated companion: namely, to provide an introduction for students and a reference for researchers to the techniques, results, and terminology of multiplicative number theory. This volume builds on the earlier one (which served as an introduction to basic, classical results) and focuses on sieve methods. This area has witnessed a number of major advances in recent years, e.g. gaps between primes, large values of Dirichlet polynomials and zero density estimates, all of which feature here. Despite the fact that the book can serve as an entry to contemporary mathematics, it remains largely self-contained, with appendices containing background or material more advanced than undergraduate mathematics. Again, exercises, of which there is a profusion, illustrate the theory or indicate ways in which it can be developed. Each chapter ends with a thorough set of references, which will be essential for all analytic number theorists.

This book colourfully examines a famous Jeffersonian document which set the precedent for the US Constitution's guarantee of religious liberty. Jefferson wrote the Virginia Statute, shepherded it through a decade-long struggle to adoption, and included it in his epitaph (along with the Declaration of Independence and the founding of the University of Virginia). The Statute's history reflects two key revolutionary principles: absolute freedom of religious conscience; and the separation of church and state. Both principles remain lively topics of debate on the contemporary religious and political scene. Papers collected here were presented at a conference sponsored by the National Endowment for the Humanities and the Virginia Foundation for the Humanities and Public Policy. Among the contributors are several of America's most prominent religious and political historians and experts on jurisprudence.

This book colourfully examines a famous Jeffersonian document which set the precedent for the US Constitution's guarantee of religious liberty. Jefferson wrote the Virginia Statute, shepherded it through a decade-long struggle to adoption, and included it in his epitaph (along with the Declaration of Independence and the founding of the University of Virginia). The Statute's history reflects two key revolutionary principles: absolute freedom of religious conscience; and the separation of church and state. Both principles remain lively topics of debate on the contemporary religious and political scene. Papers collected here were presented at a conference sponsored by the National Endowment for the Humanities and the Virginia Foundation for the Humanities and Public Policy. Among the contributors are several of America's most prominent religious and political historians and experts on jurisprudence.

Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises.