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Introduction to Analytic Number Theory (Undergraduate Texts in Mathematics) Paperback – 4 Dec 2010
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From the reviews:
Introduction to Analytic Number Theory
"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages. The presentation is invariably lucid and the book is a real pleasure to read."
“After reading Introduction to Analytic Number Theory one is left with the impression that the author, Tom M. Apostal, has pulled off some magic trick. … I must admit that I love this book. The selection of topics is excellent, the exposition is fluid, the proofs are clear and nicely structured, and every chapter contains its own set of … exercises. … this book is very readable and approachable, and it would work very nicely as a text for a second course in number theory.” (Álvaro Lozano-Robledo, The Mathematical Association of America, December, 2011)
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The first few chapters deal with "elementary" ideas, such as arithmetic functions and congruences. There is also a look at group theory and Dirichlet characters, which are relevant to L series. The book ends with a look at the partition function and infinite products, which is a really interesting and beautiful topic!
There are exercises at the end of every chapter, but unfortunately there are no answers in the back, which is a shame, because the reader cannot check if his/her work is correct.
This book has been in print for about 30 years and has deservedly attained a reputation as something of a classic, in mathematical circles.
By the way, it took me a while to figure out what the diagram on the front cover is supposed to be. It's a diagram of the GCD function (greatest common divisor).
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