Introduction to Analytic Number Theory

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Springer Science & Business Media, May 28, 1998 - Mathematics - 340 pages
4 Reviews

"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."-—MATHEMATICAL REVIEWS

 

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解析数论概论,研一下教材

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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.

Contents

Historical Introduction
1
The Fundamental Theorem of Arithmetic
13
Chapter
14
The Euclidean algorithm
19
Chapter 3
52
Chapter 4
71
Chapter 5
106
Chapter 6
129
Chapter 9
177
Primitive Roots
204
Chapter 11
223
Chapter 12
249
Chapter 13
278
Partitions
304
Bibliography
329
Index
335

Chapter 7
146
Periodic Arithmetical Functions and Gauss Sums
157

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About the author (1998)

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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