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The Great Prime Number Race
 
Roger Plymen Manchester University, Manchester, United Kingdom
The Great Prime Number Race
Softcover ISBN:  978-1-4704-6257-4
Product Code:  STML/92
List Price: $59.00
MAA Member Price: $47.20
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-6279-6
Product Code:  STML/92.E
List Price: $59.00
MAA Member Price: $47.20
AMS Member Price: $47.20
Softcover ISBN:  978-1-4704-6257-4
eBook: ISBN:  978-1-4704-6279-6
Product Code:  STML/92.B
List Price: $118.00 $88.50
MAA Member Price: $94.40 $70.80
AMS Member Price: $94.40 $70.80
The Great Prime Number Race
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The Great Prime Number Race
Roger Plymen Manchester University, Manchester, United Kingdom
Softcover ISBN:  978-1-4704-6257-4
Product Code:  STML/92
List Price: $59.00
MAA Member Price: $47.20
AMS Member Price: $47.20
eBook ISBN:  978-1-4704-6279-6
Product Code:  STML/92.E
List Price: $59.00
MAA Member Price: $47.20
AMS Member Price: $47.20
Softcover ISBN:  978-1-4704-6257-4
eBook ISBN:  978-1-4704-6279-6
Product Code:  STML/92.B
List Price: $118.00 $88.50
MAA Member Price: $94.40 $70.80
AMS Member Price: $94.40 $70.80
  • Book Details
     
     
    Student Mathematical Library
    Volume: 922020; 152 pp
    MSC: Primary 11;

    Have you ever wondered about the explicit formulas in analytic number theory? This short book provides a streamlined and rigorous approach to the explicit formulas of Riemann and von Mangoldt. The race between the prime counting function and the logarithmic integral forms a motivating thread through the narrative, which emphasizes the interplay between the oscillatory terms in the Riemann formula and the Skewes number, the least number for which the prime number theorem undercounts the number of primes. Throughout the book, there are scholarly references to the pioneering work of Euler. The book includes a proof of the prime number theorem and outlines a proof of Littlewood's oscillation theorem before finishing with the current best numerical upper bounds on the Skewes number.

    This book is a unique text that provides all the mathematical background for understanding the Skewes number. Many exercises are included, with hints for solutions. This book is suitable for anyone with a first course in complex analysis. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.

    Readership

    Undergraduate and graduate students interested in analytic number theory.

  • Table of Contents
     
     
    • Chapters
    • The Riemann zeta function
    • The Euler product
    • The functional equation
    • The explicit formulas in analytic number theory
    • The prime number theorem
    • Oscillation of $\pi (x)-\mathrm {Li}(x)$
    • The prime number race
    • Exercises, hints, and selected solutions
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 922020; 152 pp
MSC: Primary 11;

Have you ever wondered about the explicit formulas in analytic number theory? This short book provides a streamlined and rigorous approach to the explicit formulas of Riemann and von Mangoldt. The race between the prime counting function and the logarithmic integral forms a motivating thread through the narrative, which emphasizes the interplay between the oscillatory terms in the Riemann formula and the Skewes number, the least number for which the prime number theorem undercounts the number of primes. Throughout the book, there are scholarly references to the pioneering work of Euler. The book includes a proof of the prime number theorem and outlines a proof of Littlewood's oscillation theorem before finishing with the current best numerical upper bounds on the Skewes number.

This book is a unique text that provides all the mathematical background for understanding the Skewes number. Many exercises are included, with hints for solutions. This book is suitable for anyone with a first course in complex analysis. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.

Readership

Undergraduate and graduate students interested in analytic number theory.

  • Chapters
  • The Riemann zeta function
  • The Euler product
  • The functional equation
  • The explicit formulas in analytic number theory
  • The prime number theorem
  • Oscillation of $\pi (x)-\mathrm {Li}(x)$
  • The prime number race
  • Exercises, hints, and selected solutions
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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