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Analytic Number Theory for Beginners: Second Edition
 
Prapanpong Pongsriiam Silpakorn University, Nakhon Pathom, Thailand and Nagoya University, Nagoya, Japan
Softcover ISBN:  978-1-4704-6444-8
Product Code:  STML/103
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-7357-0
Product Code:  STML/103.E
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
Softcover ISBN:  978-1-4704-6444-8
eBook: ISBN:  978-1-4704-7357-0
Product Code:  STML/103.B
List Price: $118.00 $88.50
Sale Price: $70.80 $53.10
Click above image for expanded view
Analytic Number Theory for Beginners: Second Edition
Prapanpong Pongsriiam Silpakorn University, Nakhon Pathom, Thailand and Nagoya University, Nagoya, Japan
Softcover ISBN:  978-1-4704-6444-8
Product Code:  STML/103
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-7357-0
Product Code:  STML/103.E
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
Softcover ISBN:  978-1-4704-6444-8
eBook ISBN:  978-1-4704-7357-0
Product Code:  STML/103.B
List Price: $118.00 $88.50
Sale Price: $70.80 $53.10
  • Book Details
     
     
    Student Mathematical Library
    Volume: 1032023; 375 pp
    MSC: Primary 11

    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.

    Readership

    Undergraduate and graduate students interested in analytic number theory.

  • Table of Contents
     
     
    • Chapters
    • 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
  • Reviews
     
     
    • While this is a book for a first (graduate) course in analytic number theory, it contains recent results. For example, the book includes several theorems by Terrence Tao and his collaborators on primes in arithmetic progressions and on twin primes. In sum, 'Analytic Number Theory for Beginners' provides a brisk introduction to analytic number theory, with more than enough material for a graduate course.

      John D. Cook, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1032023; 375 pp
MSC: Primary 11

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.

Readership

Undergraduate and graduate students interested in analytic number theory.

  • Chapters
  • 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
  • While this is a book for a first (graduate) course in analytic number theory, it contains recent results. For example, the book includes several theorems by Terrence Tao and his collaborators on primes in arithmetic progressions and on twin primes. In sum, 'Analytic Number Theory for Beginners' provides a brisk introduction to analytic number theory, with more than enough material for a graduate course.

    John D. Cook, MAA Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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