An Introduction to the Theory of the Riemann Zeta-Function (Cambridge Studies in Advanced Mathematics) [Paperback]

S. J. Patterson (Author)

Book Description

ISBN-10: 0521499054 | ISBN-13: 978-0521499057 | Publication Date: February 24, 1995

This is a modern introduction to the analytic techniques used in the investigation of zeta-function. Riemann introduced this function in connection with his study of prime numbers, and from this has developed the subject of analytic number theory. Since then, many other classes of "zeta-function" have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasized central ideas of broad application, avoiding technical results and the customary function-theoretic approach.

Editorial Reviews

Book Description

This modern introduction to the analytic techniques used in the investigation of zeta-function avoids technical results and the customary function-theoretic approach. Since Riemann's introduction, many other classes of "zeta-function" have been introduced and are now intensively studied.

Product Details

• Paperback: 172 pages
• Publisher: Cambridge University Press (February 24, 1995)
• Language: English
• ISBN-10: 0521499054
• ISBN-13: 978-0521499057
• Product Dimensions: 8.8 x 5.9 x 0.5 inches
• Shipping Weight: 9.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #620,719 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

39 of 39 people found the following review helpful:

4.0 out of 5 stars An excellent resource for those interested in Riemann's, April 11, 2003

By 

Steven E Macks (Roseville, Minnesota) - See all my reviews

This review is from: An Introduction to the Theory of the Riemann Zeta-Function (Cambridge Studies in Advanced Mathematics) (Paperback)

Zeta function. This book contains a lot of application, theory, and, to my surprise, several practice problems at the end of each section to maximize the learning experience. The chapters are concise and the mathematics is relatively easy follow for those with some experience in special functions.
That, however, is the major thing to note: one needs some experience with special functions in order to find this material accessible. (Obviously, right? Otherwise one wouldn't be buying this book! However, much of this material is beyond the grasp of the average mathematics student that stopped at a bachelor's degree.)
Although this book is called an introduction, I don't think that view is entirely appropriate. The material is quite extensive, and the historocity of the zeta function and its development were kept to a minimum. The precursors to the zeta function and its development by Euler and Riemann (especially Euler's original proof to the Basel Problem) are fantastic. If you're interested in Euler's role in the development, I would look to Dunham's Euler: The Master of Us All, and for Riemann, one should turn to Edwads' Riemann's Zeta Function to read Riemann's original paper.
If you're looking for depth, conciseness, and a broad view of Riemann's zeta function, this book should suit your purposes. If you want a more historical view, I would suggest either of the other books I've mentioned, and not this one.

8 of 8 people found the following review helpful:

5.0 out of 5 stars Analytic Number Theory through Zeta-Function, January 28, 2007

By 

Paul Jolissaint "analytic paul" - See all my reviews
(REAL NAME)   

This review is from: An Introduction to the Theory of the Riemann Zeta-Function (Cambridge Studies in Advanced Mathematics) (Paperback)

This introductory textbook gives a very good insight of analytic number theory through the special topic of Riemann Zeta-Function. It also includes of course an excellent exposition of its relationship with the Prime Number Theorem and with Riemann and Lindelöf Hypotheses. Moreover, seven appendices provide analytic technical complements needed in the core of the text. Many well-chosen exercises and problems accompany each chapter. I use this textbook in my course on Zeta-Function with great success.