Multiplicative Number Theory I: Classical Theory
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.
1100959787
Multiplicative Number Theory I: Classical Theory
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.
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Multiplicative Number Theory I: Classical Theory

Multiplicative Number Theory I: Classical Theory

Multiplicative Number Theory I: Classical Theory

Multiplicative Number Theory I: Classical Theory

Overview

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.

Product Details

ISBN-13: 9780521849036
Publisher: Cambridge University Press
Publication date: 11/16/2006
Series: Cambridge Studies in Advanced Mathematics , #97
Edition description: New Edition
Pages: 572
Product dimensions: 6.38(w) x 8.94(h) x 1.42(d)

About the Author

Hugh Montgomery is a Professor of Mathematics at the University of Michigan.

Robert Vaughan is a Professor of Mathematics at Pennsylvannia State University.

Table of Contents

Preface; Notation; 1. Dirichlet series-I; 2. The elementary theory of arithmetic functions; 3. Principles and first examples of sieve methods; 4. Primes in arithmetic progressions-I; 5. Dirichlet series-II; 6. The prime number theorem; 7. Applications of the prime number theorem; 8. Further discussion of the prime number theorem; 9. Primitive characters and Gauss sums; 10. Analytic properties of the zeta function and L-functions; 11. Primes in arithmetic progressions-II; 12. Explicit formulae; 13. Conditional estimates; 14. Zeros; 15. Oscillations of error terms; Appendix A. The Riemann-Stieltjes integral; Appendix B. Bernoulli numbers and the Euler-MacLaurin summation formula; Appendix C. The gamma function; Appendix D. Topics in harmonic analysis.

What People are Saying About This

From the Publisher

"The monograph is a very readable, concise presentation of classical prime number theory, giving techniques as well as the underlying ideas, and describing an incredibly large range of topics. A study of this monograph seems to be a must for every number theorist. Hopefully this volume will be available as soon as possible, to renew and broaden the interest in this highly interesting field of analytic prime number theory."
Wolfgang Schwarz, Mathematical Reviews

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