Multiplicative Number Theory I : Classical Theory

by Montgomery, Hugh L.; Vaughan, Robert C.

• ISBN13: 9781107405820
• ISBN10: 1107405823
• Edition: Reprint
• Format: Paperback
• Copyright: 2012-07-26
• Publisher: Cambridge Univ Pr

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

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