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

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

Customer Rating:
Summary: Analytic Number Theory through Zeta-Function
Comment: 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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Customer Rating:
Summary: An excellent resource for those interested in Riemann's
Comment: 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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