Introduction to Analytic Number Theory, Volume 1

Front Cover
Springer, May 11, 1976 - Mathematics - 338 pages
4 Reviews
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. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include Dirichlet's theorem on primes in progressions, Gauss sums, quadratic residues, Dirichlet series, and Euler products with applications to the Riemann zeta function and Dirichlet L-functions. Also included is an introduction to partitions. 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.

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I've found this to be the best overall introduction to analytic number theory. I'm trained in physics, and interested in number theory, and this book really helped me to learn the basics. The problems are excellent as well.

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This is the best book I ever found in Analytic Number Theory. It had given history of number theory in brief, which is also inspiring. Chapter 1 deals with Fundamental Theorem of Arithmetic. In this chapter divisiblity, greatest common factor, prime numbers etc etc are explained in very nice manner.
The arrangement of chapters are very nice. It starts with easy topics and ending with more difficult chapters. I would like to say that this is topmost beautiful book in area of NUMBER THEORY.

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Historical Introduction
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Chapter 7
Periodic Arithmetical Functions and Gauss Sums

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References to this book

Permutation Groups
John D. Dixon
Limited preview - 1996
Tom M. Apostol
No preview available - 1990
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JSTOR: Introduction to Analytic Number Theory
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Analytic number theory - Wikipedia, the free encyclopedia
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Dickson le.djvu 12 Mb; Introduction To Analytic Number Theory - Apostol.pdf 13 Mb; Introduction to Modern Number Theory Fundamental Problems, ... eac4a1480c01f20373013974838bcff4aa5f70bd

MAT 311 - Number Theory -- Spring 2004
... Number Theory, ge Andrews; Introduction to Analytic Number Theory, tm Apostol; Lectures on Number Theory, pgl Dirichlet with supplements by R. Dedekind ... ~sorin/ 311-2004/

About the author (1976)

Tom M. Apostol joined the California Institute of Technology faculty in 1950 and is now Professor of Mathematics, Emeritus. He is internationally known for his textbooks on Calculus, Analysis, and Analytic Number Theory, which have been translated into 5 languages, and for creating Project MATHEMATICS!, a series of video programs that bring mathematics to life with computer animation, live action, music, and special effects. The videos have won first-place honors at a dozen international video festivals, and have been translated into Hebrew, Portuguese, French, and Spanish. His list of publications includes 98 research papers, 46 of them published since he retired in 1992. He has received several awards for his research and teaching. In 1978 he was a visiting professor at the University of Patras in Greece, and in 2000 was elected a Corresponding Member of the Academy of Athens, where he delivered his inaugural lecture in Greek.

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