Multiplicative Number Theory I : Classical Theory
by Montgomery, Hugh L.; Vaughan, Robert C.Edition: Reprint
Format: Paperback
Pub. Date: 2012-07-26
Publisher(s): Cambridge Univ Pr
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Summary
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. This book comprehensively covers all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. The text is based on courses taught successfully over many years at the University of Michigan, Imperial College, London and Pennsylvania State University.
Table of Contents
| Preface | |
| Notation | |
| Dirichlet series-I | |
| The elementary theory of arithmetic functions | |
| Principles and first examples of sieve methods | |
| Primes in arithmetic progressions-I | |
| Dirichlet series-II | |
| The prime number theorem | |
| Applications of the prime number theorem | |
| Further discussion of the prime number theorem | |
| Primitive characters and Gauss sums | |
| Analytic properties of the zeta function and L-functions | |
| Primes in arithmetic progressions-II | |
| Explicit formulae | |
| Conditional estimates | |
| Zeros | |
| Oscillations of error terms | |
| The Riemann-Stieltjes integral | |
| Bernoulli numbers and the Euler-MacLaurin summation formula | |
| The gamma function | |
| Topics in harmonic analysis | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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