Multiplicative Number Theory I: Classical Theory

Description

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. The 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.

Hugh Montgomery is a Professor of Mathematics at the University of Michigan. Robert Vaughan is a Professor of Mathematics at Pennsylvannia State University.

'The text is very well written and accessible to students. On many occasions the authors explicitly describe basic methods known to everyone working in the field, but too often skipped in textbooks. This book may well become the standard introduction to analytic number theory.' Zentralblatt MATH