Analytic number theory for beginners
著者
書誌事項
Analytic number theory for beginners
（Student mathematical library, v. 103）
American Mathematical Society, c2023
2nd ed
- : pbk
- タイトル別名
-
Introduction to analytic number theory
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注記
First ed. published: Nakhon Pathom : Silpakorn University Printinghouse, 2020
Includes bibliographical references (p. 347-366) and indexes
内容説明・目次
内容説明
This new edition of Analytic Number Theory for Beginners presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, and offers a comfortable transition between the two levels. The text starts with a review of elementary number theory and continues on to present less commonly covered topics such as multiplicative functions, the floor function, the use of big $O$, little $o$, and Vinogradov notation, as well as summation formulas. Standard advanced topics follow, such as the Dirichlet $L$-function, Dirichlet's Theorem for primes in arithmetic progressions, the Riemann Zeta function, the Prime Number Theorem, and, new in this second edition, sieve methods and additive number theory.
The book is self-contained and easy to follow. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes which include a chapter summary, open questions, historical background, and resources for further study. Since many topics in this book are not typically covered at such an accessible level, Analytic Number Theory for Beginners is likely to fill an important niche in today's selection of titles in this field.
目次
Review of elementary number theory
Arithmetic functions I
The floor function
Summation formulas
Arithmetic functions II
Elementary results on the distribution of primes
Characters and Dirichlet's theorem
The Riemann zeta function
Prime number theorem and some extensions
Introduction to other topics
Hints for selected exercises
Bibliography
Subject index
Name Index
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