Analytic Number Theory (Graduate Texts in Mathematics) | 
 enlarge | Author: Donald J. Newman
Publisher: Springer
Category: Book
List Price: $49.95
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Rating:  2 reviews
Sales Rank: 1061365
Media: Hardcover
Edition: Corrected
Pages: 78
Number Of Items: 1
Shipping Weight (lbs): 0.7
Dimensions (in): 9.6 x 6.5 x 0.4
ISBN: 0387983082
Dewey Decimal Number: 512.73
EAN: 9780387983080
Publication Date: July 19, 2000
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Product Description
Analytic Number Theory presents some of the central topics in number theory in a simple and concise fashion. It covers an amazing amount of material, despite the leisurely pace and emphasis on readability. The author's heartfelt enthusiasm enables readers to see what is magical about the subject. Topics included are: The Partition Function; The Erdoes-Fuchs Theorem; Sequences without Arithmetic Professions; The Waring Problem; A "Natural" Proof of the Non-vanishing of L-Series, and a Simple Analytic Proof of the Prime Number Theorem - all presented in a surprisingly elegant and efficient manner with clever examples and interesting problems in each chapter. This text is suitable for a graduate course in analytic number theory.
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| Customer Reviews:
Second printing corrects most typos April 26, 2002
5 out of 5 found this review helpful
This book is somewhat in the spirit of Aigner and Ziegler's "Proofs from the Book": short, clear proofs of important results in Analytic Number Theory. My favorite parts are (1) the "natural" proof of the non-vanishing of L-series, which really does make it look inevitable; (2) the Crazy Dice, a simple and surprising example of the power that generating functions provide when you switch your viewpoint between formal power series and the functions they represent.To some extent the author keeps the proofs short by leaving out steps, so you'll need to read it with pencil and paper nearby to work out the missing steps. The first printing was loaded with typographical errors; most (not all) of these are corrected in the 2000 second printing. Unfortunately not all the remaining typos are obviously typos; this combined with the brevity can make the exposition hard to follow. The first printing was fascinating (for its content) and exasperating (for its typos); the second printing is still fascinating, and occasionally exasperating.
Excellent book, very clear. A few errors still. June 13, 2006
Alexander C. Zorach (New Haven, CT)
1 out of 1 found this review helpful
I find this book exceptionally clear. It's the thinnest GTM text I've ever seen, but there is a lot of material there.
It's true that this book doesn't have a comprehensive treatment of analytic number theory, I like the other reviewer's analogy of an appendix to generatingfunctionology--this book does focus primarily on sequences and generating functions. However, it is a very clear, fun, and easy to read book. The book's thinness may be misleading; there is plenty of explanatory prose, motivation, discussion, and proofs are generally pretty easy to follow.
The revised printing does correct many errors, but I was still able to find some (and I suspect this means there are a lot more than I was able to find). This was a little bit annoying, but only a little bit. Overall I think this is a great book.
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