Introduction to Analytic Number Theory

by Tom M. Apostol

This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus.

Genres: Mathematics, Number Theory, Science, Nonfiction, Textbooks, Theory, Number

352 pages, Hardcover

First published January 1, 1976

Reviews

[Hobart Mariner]

An exercise in good taste: selection of topics, exercises/problems, computational example. Maybe the best intro to any subject I've read...better than baby Rudin even. A great deal of affection for the subject shines through, even though the author refrains from the corny humor and rantiness that plague lesser books. Genuinely a stone classic, readable by almost anyone (until you get to the complex analytic bits in the later chapters), and successful in conveying the vibe, beauty, and meaning of its subject.

[Nilo De Roock]

The Open University UK, which is truly excellent in writing their own study materials, used this book as a prime reading source for their analytic number theory courses M823 and M829 at the MSC. level. That should say enough about the quality of the text. - Everytime I pick up this book, it is with joy, and, there is always the likelyhood of learning the material at a deeper level.

[Marianna]

This book is OK when the reader is quite familiar with number theory's methods, but it doesn't expose aftermaths as clearly as you'd expect from an undergraduate book. If it's just the first time you approach to the subject you better look for other books as well.

[Wissam Raji]

A very good undergraduate introductory book to analytic number theory. The treatment is basic and understandable for those who have basic knowledge of real analysis. The topics chosen are carefully chosen and explicitly dealt with. Highly recommended for those who want to learn analytic number theory.

[Ayush Bhat]

It's a classic, no doubt about that but, it doesn't go deep into stuff just touches then leaves the topic.

[Cương Trần]

I want to read this book, please!
Thanks!

[Andrew]

Brilliant! Expertly written and full of fascinating number theory - working towards understanding the mathematics behind the Prime Number Theorem and Riemann Hypothesis.

[Satyaki]

https://www.youtube.com/playlist?list...

[Elizabeth S. Q. Goodman]

I figure I need some grounding in analytic number theory, because I've always found it confusing. I read the first two chapters or so of this and that was fine.