Hardcover ISBN:  9781470417062 
Product Code:  GSM/160 
List Price:  $84.00 
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AMS Member Price:  $67.20 
Electronic ISBN:  9781470420413 
Product Code:  GSM/160.E 
List Price:  $79.00 
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AMS Member Price:  $63.20 

Book DetailsGraduate Studies in MathematicsVolume: 160; 2014; 371 ppMSC: Primary 11;
This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the SiegelWalfisz theorem, functional equations of Lfunctions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem.
The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader.
The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.ReadershipGraduate students interested in number theory.

Table of Contents

Chapters

Chapter 1. Arithmetic functions

Chapter 2. Topics on arithmetic functions

Chapter 3. Characters and Euler products

Chapter 4. The circle method

Chapter 5. The method of contour integrals

Chapter 6. The prime number theorem

Chapter 7. The SiegelWalfisz theorem

Chapter 8. Mainly analysis

Chapter 9. Euler products and number fields

Chapter 10. Explicit formulas

Chapter 11. Supplementary exercises


Additional Material

Reviews

This book is a proper text for a graduate student (with a pretty strong background) keen on getting into analytic number theory, and it's quite a good one. It's wellwritten, rather exhaustive, and wellpaced. The choice of themes is good, too, and will form a very sound platform for future studies and work in this gorgeous field.
MAA Reviews


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This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the SiegelWalfisz theorem, functional equations of Lfunctions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem.
The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader.
The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.
Graduate students interested in number theory.

Chapters

Chapter 1. Arithmetic functions

Chapter 2. Topics on arithmetic functions

Chapter 3. Characters and Euler products

Chapter 4. The circle method

Chapter 5. The method of contour integrals

Chapter 6. The prime number theorem

Chapter 7. The SiegelWalfisz theorem

Chapter 8. Mainly analysis

Chapter 9. Euler products and number fields

Chapter 10. Explicit formulas

Chapter 11. Supplementary exercises

This book is a proper text for a graduate student (with a pretty strong background) keen on getting into analytic number theory, and it's quite a good one. It's wellwritten, rather exhaustive, and wellpaced. The choice of themes is good, too, and will form a very sound platform for future studies and work in this gorgeous field.
MAA Reviews