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Introduction to Analytic and Probabilistic Number Theory (Cambridge Studies in Advanced Mathematics) Hardcover – June 30, 1995

ISBN-13: 978-0521412612 ISBN-10: 0521412617

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Product Details

  • Series: Cambridge Studies in Advanced Mathematics (Book 46)
  • Hardcover: 468 pages
  • Publisher: Cambridge University Press (June 30, 1995)
  • Language: English
  • ISBN-10: 0521412617
  • ISBN-13: 978-0521412612
  • Product Dimensions: 6 x 1.2 x 9 inches
  • Shipping Weight: 1.7 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: #1,328,070 in Books (See Top 100 in Books)

Editorial Reviews


"Gerald Tenenbaum has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate."
H.G. Diamond, Mathematical Reviews

"It contains clear and well written text, and enough exercises. I can recommend this book for students, researchers and professors, for studying and teaching."
Mehdi Hassani, MAA Reviews

Language Notes

Text: English (translation)
Original Language: French

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Most Helpful Customer Reviews

4 of 4 people found the following review helpful By Gilles Benson on March 22, 2008
Format: Hardcover
I am very much in tune with everything that has already been written on this book although I don't feel that the text is that conventional; the author has chosen to separate every chapter in three parts: 1) theorems and proofs according to the chapter's title; 2) notes on the chapter which may contain additional theorems and proofs. 3) exercices enhancing the first part. It is said (I did not try them...) that the exercices are really challenging; this can be expected since the main subject of this book is very challenging: arithmetic functions are notoriously very bad behaving functions with very erratic asymptotic properties (for example: the Euler phi-function). One good news is that a solution book exists (although written in french) which can be found on the site of the SMF (Société mathématiques de france); another good news is that a third vastly augmented edition can also be found on French book sites at a much cheaper price than Cambridge's: Introduction à la théorie analytique et probabiliste des nombres (Belin 2008). And mathematical french is not that daunting.
The text is rather self-contained since the main tools of the trade are given in the first chapters and there is a whole chapter on Euler Gamma function with a view towards Mellin transform and Stirling formula.
As a reward for all the "hard work" needed to grovel through the book, one can find a whole chapter discussing Riemann's long standing hypothesis; one of the main reference on the subject; earlier works that I would suggest are "Arithmetical functions" by Chandrasekharan (Springer 1970) and "Les nombres premiers" by W.J. Ellison (Hermann 1975) which has been translated in english in 1985.
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6 of 9 people found the following review helpful By Satanas on February 17, 2000
Format: Hardcover
Gerald Tenenbaum's lucid writing style provides a comprehensive, yet non-painful introduction to the subject. This book focuses on methods, which once learned are of utility both to the expert and novice. The beautiful---and sometimes obscure results---chosen as exercises enhance the appeal of the book. A must for number theorists and a text for anyone wanting to explore applications of analysis in an arithmetic setting.
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