The Theory of the Riemann Zeta-Function (Oxford Science Publications) [Paperback]

E. C. Titchmarsh (Author), D. R. Heath-Brown (Editor)

Book Description

ISBN-10: 0198533691 | ISBN-13: 978-0198533696 | Publication Date: February 5, 1987 | Edition: 2

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects of the theory, starting from first principles and probing the function's own challenging theory, with the famous and still unsolved "Riemann hypothesis" at its heart. The second edition has been revised to include descriptions of work done in the last forty years and is updated with many additional references; it will provide stimulating reading for postgraduates and workers in analytic number theory and classical analysis.

Editorial Reviews

Review

"The first edition of this classical treatise appeared in 1951 . . . Besides writing the updating and elucidating notes, covering all in all over 50 pages, the editor also has compiled a list of some 120 additional references to the more recent literature on the zeta-function. Thanks to the ample new material, this new edition makes very interesting reading, even for those who are familiar with the original." --Mathematical Reviews

"A reprinting of this classic treatise with corrections and extensive end-of-chapter notes by D.R. Heath-Brown." --The American Mathematical Monthly

About the Author

The late E.C. Titchmarsh was at University of Oxford. D. R. Heath-Brown is at Magdelen College, Oxford.

Product Details

• Paperback: 422 pages
• Publisher: Oxford University Press, USA; 2 edition (February 5, 1987)
• Language: English
• ISBN-10: 0198533691
• ISBN-13: 978-0198533696
• Product Dimensions: 9.2 x 6.2 x 1 inches
• Shipping Weight: 1.5 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,309,647 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

18 of 19 people found the following review helpful:

5.0 out of 5 stars Complete source of the zeta function, January 18, 2004

By 

J. N. M. ROBLES "Nicolas M. Robles" (London, UK) - See all my reviews
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This review is from: The Theory of the Riemann Zeta-Function (Oxford Science Publications) (Paperback)

This is the true encyclopaedia of the zeta function. Although I prefer Ivic, I always have the feeling that Titchmarsh wants to appear brilliant.

This book cannot be criticized because of the amount of time and effort that must have been spent on it. It was update in 1986 by Heath Brown.
It is useless to summarize the contents because it mainly has everything, and most theorems have several proofs and very long comments.
One thing that is missing is more stuff about prime number distributions (for this, check Ingham, Edward's, and a bit of Ivic's).

It never becomes redundant, and it can either be used a source for additional information, as dictionary, or it can be used in a linear way.

11 of 13 people found the following review helpful:

5.0 out of 5 stars An very comprehesive book for Zeta Function., August 22, 2001

By 

Wan Koon Yat "wankoonyat" (North Point Hong Kong) - See all my reviews
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Amazon Verified Purchase

This review is from: The Theory of the Riemann Zeta-Function (Oxford Science Publications) (Paperback)

Titchmarch is well known in the theory of functions, in this book, he described the Riemann's Zeta function in the most comprehensive way. ( e. g. in the topic of functional equation, he quoted 7 methods) I cannot find any other book more comprehensive than this one. ( though in order the theories, you must have some background knowledge and patience ! )