**Graduate Studies in Mathematics**

Volume: 160;
2014;
371 pp;
Hardcover

MSC: Primary 11;

Print ISBN: 978-1-4704-1706-2

Product Code: GSM/160

List Price: $79.00

AMS Member Price: $63.20

MAA member Price: $71.10

**Electronic ISBN: 978-1-4704-2041-3
Product Code: GSM/160.E**

List Price: $79.00

AMS Member Price: $63.20

MAA member Price: $71.10

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#### Supplemental Materials

# A Course in Analytic Number Theory

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*Marius Overholt*

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
Siegel-Walfisz theorem, functional equations of L-functions, 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.

#### Readership

Graduate students interested in number theory.

#### Reviews & Endorsements

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 well-written, rather exhaustive, and well-paced. 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

#### Table of Contents

# Table of Contents

## A Course in Analytic Number Theory

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface xi12 free
- Acknowledgments xiii14 free
- How to use this text xv16 free
- Introduction xvii18 free
- Chapter 1. Arithmetic functions 120 free
- Chapter 2. Topics on arithmetic functions 4160
- Chapter 3. Characters and Euler products 5978
- Chapter 4. The circle method 111130
- Chapter 5. The method of contour integrals 157176
- Chapter 6. The prime number theorem 169188
- Chapter 7. The Siegel-Walfisz theorem 183202
- Chapter 8. Mainly analysis 209228
- Chapter 9. Euler products and number fields 255274
- Chapter 10. Explicit formulas 307326
- Chapter 11. Supplementary exercises 327346
- Bibliography 341360
- List of notations 357376
- Index 363382 free
- Back Cover Back Cover1394