Multiplicative Number Theory [Hardcover]

Harold Davenport (Author), H.L. Montgomery (Editor)

Book Description

ISBN-10: 0387950974 | ISBN-13: 978-0387950976 | Publication Date: October 31, 2000 | Edition: 3nd

The new edition of this thorough examination of the distribution of prime numbers in arithmetic progressions offers many revisions and corrections as well as a new section recounting recent works in the field. The book covers many classical results, including the Dirichlet theorem on the existence of prime numbers in arithmetical progressions and the theorem of Siegel. It also presents a simplified, improved version of the large sieve method.

Editorial Reviews

Review

From the reviews of the third edition: "The book under review is one of the most important references in the multiplicative number theory, as its title mentions exactly. … Davenport’s book covers most of the important topics in the theory of distribution of primes and leads the reader to serious research topics … . is very well written. … is useful for graduate students, researchers and for professors. It is a very good text source specially for graduate levels, but even is fruitful for undergraduates." (Mehdi Hassani, MathDL, July, 2008)

Product Details

• Hardcover: 177 pages
• Publisher: Springer; 3nd edition (October 31, 2000)
• Language: English
• ISBN-10: 0387950974
• ISBN-13: 978-0387950976
• Product Dimensions: 9.3 x 6.2 x 0.7 inches
• Shipping Weight: 10.4 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #157,277 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

27 of 27 people found the following review helpful:

5.0 out of 5 stars A good historical approach to Analytic Number Theory, December 25, 2000

By A Customer

This review is from: Multiplicative Number Theory (Hardcover)

I like this book because it gives you a good understanding of where the difficulties in the subject are. It takes a historical approach, following more or less the same steps that the original discoverers of these results took. Today we have very slick proofs for many of these results, and it is sometimes hard to understand why it took so long to discover them in the first place, but this book will give you this understanding; Dirichlet in particular practically had to invent Analytic Number Theory to prove his theorem on primes in an arithmetic progression.

The book works up gradually to each result, for example proving Dirichlet's theorem first for a prime modulus (as Dirichlet did himself), then the general modulus. In most cases it proves first the result for all primes (zeta function) and then the generalization for primes in an arithmetic progression (L function), pointing out which parts generalize easily and which cause special difficulties.

Some of the more advanced results covered are exponential sums, Vinogradov's theorem that every large odd number is the sum of three primes, and Bombieri's theorem about the average distribution of primes in arithmetic progressions.

I haven't seen the previous (1980) edition; this new edition seems to be lightly revised from the previous one. The last chapter is up-to-date and gives a brief survey of new results and of new books on the subject.

20 of 22 people found the following review helpful:

5.0 out of 5 stars An extraordinary Book, June 11, 2002

By 

"orca137" (Mansfield, PA USA) - See all my reviews

This review is from: Multiplicative Number Theory (Hardcover)

Ever since I first read about the prime number theorem, I have been roaming the mathetmatical landscape, looking for the best proof of this result. I believe this book has it. It's not the simplest or the shortest proof, but it gives the deepest understanding of why the prime numbers behve like they do. In addition to this, it shows you the historical perspective in these proofs. All too often today math books give one short and slick proofs that leave you wondering how on earth they came up with it. In this book, however, one can almost feel the thoughts going through Riemann and Dirichlet's heads as they came up with the theorems. This book also has the proof of Dirichlet's theorem and Vinogradov's partial proof of the ternary goldbach conjecture. The vinogradov and following sections are considerably harder, partly because they were not written by Davenport himself. Anyway, if you're serious about Analytic number theory and how mathematicians think, this books needs to be on your bookshelf.

4 of 4 people found the following review helpful:

5.0 out of 5 stars If you want to be an analytic number theorist, March 12, 2010

By 

Narada "the wondering jew" (Princeton, NJ, USA) - See all my reviews
(VINE VOICE)   

This review is from: Multiplicative Number Theory (Hardcover)

Work through this book. While Serre's A Course in Arithmetic (Graduate Texts in Mathematics) is slicker, it is nowhere near as enlightening. Iwaniec's treatise Analytic Number Theory (Colloquium Publications, Vol. 53) (Colloquium Publications (Amer Mathematical Soc)) is a good reference for professionals, but unreadable for someone who has not seen (a lot of) the material before. Davenport's book is very clear and very deep at the same time. The recent editions of this book have been brought up to date, but the core has not changed too much, so don't feel obligated to buy the latest edition.