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

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ISBN-13: 978-0521499057
ISBN-10: 0521499054
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An Introduction to the Theory of the Riemann Zeta-Function (Cambridge Studies in Advanced Mathematics) + Riemann's Zeta Function + The Riemann Zeta-Function: Theory and Applications (Dover Books on Mathematics)
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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.

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Product Details

  • Series: Cambridge Studies in Advanced Mathematics (Book 14)
  • Paperback: 172 pages
  • Publisher: Cambridge University Press (February 24, 1995)
  • Language: English
  • ISBN-10: 0521499054
  • ISBN-13: 978-0521499057
  • Product Dimensions: 6 x 0.4 x 9 inches
  • Shipping Weight: 11.4 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: #1,940,758 in Books (See Top 100 in Books)

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43 of 43 people found the following review helpful By Steven E Macks on April 11, 2003
Format: 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.
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10 of 10 people found the following review helpful By Paul Jolissaint on January 28, 2007
Format: 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.
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An Introduction to the Theory of the Riemann Zeta-Function (Cambridge Studies in Advanced Mathematics)
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