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Rating: 
Summary: Nice little book if you ignore all the misprints.
Review: A more appropriate title would have been "Applications of Generating Functions to Number Theory". The author has a way of making some difficult proofs look very natural, almost obvious, and the choice of material includes many deep and well known theorems in number theory, including the author's own simple proof of the Prime Number Theorem (the shortest proof published).
The only problem with this little book (73 pages) is the ridiculously large number of misprint (Hence the rating). From the copyright notes I read the book was photocomposed from the author's LaTeX files. Well, it seems no one, not even the author himself, ever read a printout of those files. There are spelling errors, grammar mistakes, and, worse of all, wrong formulas. Some of the misprints are the result of badly typed LaTeX, something that even someone with little mathematical knowledge could spot on the fly. For example, equation (7) in chapter 2 ends with "/lec", but it should be "\le c", which is TeX's way of saying "<= c". In Chapter 3 almost all the integrals have an absent upper limit (it should be pi). Upon closer examination you discover that the author forgot to include the '^' symbol before pi (in the LaTex file), and therefore pi shows as a *factor* in the integrand. I could go on and on listing similar errors, but I guess the picture is clear. It is really a shame that Springer published this book without doing any proofreading first. If they have any ethics, they should "recall" the book and print a revised edition, with apologies from the author ;-)
Rating:
Summary: Nice little book if you ignore all the misprints.
Review: A more appropriate title would have been "Applications of Generating Functions to Number Theory". The author has a way of making some difficult proofs look very natural, almost obvious, and the choice of material includes many deep and well known theorems in number theory, including the author's own simple proof of the Prime Number Theorem (the shortest proof published).
The only problem with this little book (73 pages) is the ridiculously large number of misprint (Hence the rating). From the copyright notes I read the book was photocomposed from the author's LaTeX files. Well, it seems no one, not even the author himself, ever read a printout of those files. There are spelling errors, grammar mistakes, and, worse of all, wrong formulas. Some of the misprints are the result of badly typed LaTeX, something that even someone with little mathematical knowledge could spot on the fly. For example, equation (7) in chapter 2 ends with "/lec", but it should be "\le c", which is TeX's way of saying "<= c". In Chapter 3 almost all the integrals have an absent upper limit (it should be pi). Upon closer examination you discover that the author forgot to include the '^' symbol before pi (in the LaTex file), and therefore pi shows as a *factor* in the integrand. I could go on and on listing similar errors, but I guess the picture is clear. It is really a shame that Springer published this book without doing any proofreading first. If they have any ethics, they should "recall" the book and print a revised edition, with apologies from the author ;-)
Rating: 
Summary: Second printing corrects most typos
Review: This book has a fair number of errors (as was noted by another reviewer), but I still found it to be an enjoyable read. It *is* fairly conversational, and not complete. This book might be better suited as an apendix to Herbert Wilf's GeneratingFunctionality (no, the one word is not a misprint). There are other techniques in analytic number theory, but they are hardly touched upon. I recommend Apostol's book on the subject in lieu of this book (more complete, just as readable, and fewer errors).
Rating: 
Summary: Despite the errors, not horrible
Review: This book has a fair number of errors (as was noted by another reviewer), but I still found it to be an enjoyable read. It *is* fairly conversational, and not complete. This book might be better suited as an apendix to Herbert Wilf's GeneratingFunctionality (no, the one word is not a misprint). There are other techniques in analytic number theory, but they are hardly touched upon. I recommend Apostol's book on the subject in lieu of this book (more complete, just as readable, and fewer errors).
Rating:
Summary: Second printing corrects most typos
Review: 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.
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