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The Theory of the Riemann Zeta-Function (Oxford Science Publications) 2nd Edition

4.7 out of 5 stars 6 customer reviews
ISBN-13: 978-0198533696
ISBN-10: 0198533691
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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.
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Product Details

  • Series: Oxford Science Publications
  • Paperback: 422 pages
  • Publisher: Oxford University Press; 2 edition (February 5, 1987)
  • Language: English
  • ISBN-10: 0198533691
  • ISBN-13: 978-0198533696
  • Product Dimensions: 9.2 x 0.9 x 6.2 inches
  • Shipping Weight: 1.7 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (6 customer reviews)
  • Amazon Best Sellers Rank: #950,013 in Books (See Top 100 in Books)

Customer Reviews

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Top Customer Reviews

By J. N. M. ROBLES on January 18, 2004
Format: 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.
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I've read meticulously the chapters in this book on the functional equation of the zeta function, the prime number theorem, the approximate functional equation, the order of the zeta function in the critical strip, and the Dirichlet divisor problem (which can be expressed as a question about the square of the zeta function), and also a sprinkling of material from some of the other chapters. This is not a bad book to learn from, but the author's ways of speaking are not always modern. I think that a reader who wants to learn the analytic theory of the zeta function would do better to read Ivic's "The Riemann Zeta-Function: Theory and Applications" or Edwards' "Riemann's Zeta Function". Edwards' book does not have as much material as either Ivic or Titchmarsh but it presents the material in a historical setting. Both Ivic's book and Edwards' book are published by Dover and thus are quite cheap. For a really modern presentation of the analytic theory of the Riemann zeta function (and other L-functions, both L-functions for Dirichlet characters and for modular forms), dip into Iwaniec and Kowalski's "Analytic Number Theory". For example, Iwaniec and Kowalski prove an approximate functional equation for general L-functions that uses smoothing functions, which is not a technique that Titchmarsh uses.
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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 ! )
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