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The Riemann Hypothesis

MAA Press: An Imprint of the American Mathematical Society
Available Formats:
Softcover ISBN: 978-0-88385-650-5
Product Code: NML/46
List Price: $45.00 MAA Member Price:$33.75
AMS Member Price: $33.75 Electronic ISBN: 978-0-88385-989-6 Product Code: NML/46.E List Price:$45.00
MAA Member Price: $33.75 AMS Member Price:$33.75
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AMS Member Price: $50.63 Click above image for expanded view The Riemann Hypothesis MAA Press: An Imprint of the American Mathematical Society Available Formats:  Softcover ISBN: 978-0-88385-650-5 Product Code: NML/46  List Price:$45.00 MAA Member Price: $33.75 AMS Member Price:$33.75
 Electronic ISBN: 978-0-88385-989-6 Product Code: NML/46.E
 List Price: $45.00 MAA Member Price:$33.75 AMS Member Price: $33.75 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$67.50 MAA Member Price: $50.63 AMS Member Price:$50.63
• Book Details

Anneli Lax New Mathematical Library
Volume: 462015; 144 pp
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2018!

The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 … Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line. Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions.

The present book is a first exploration of this fascinating, unknown world. It originated from an online course for mathematically talented secondary school students organized by the authors of this book at the University of Amsterdam. Its aim was to bring the students into contact with challenging university level mathematics and show them what the Riemann Hypothesis is all about and why it is such an important problem in mathematics.

• Chapters
• Chapter 1. Prime numbers
• Chapter 2. The zeta function
• Chapter 3. The Riemann hypothesis
• Chapter 4. Primes and the Riemann hypothesis
• Appendix A. Why big primes are useful
• Appendix B. Computer support
• Appendix C. Further reading and internet surfing
• Appendix D. Solutions to the exercises

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 462015; 144 pp
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2018!

The Riemann hypothesis concerns the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 … Ubiquitous and fundamental in mathematics as they are, it is important and interesting to know as much as possible about these numbers. Simple questions would be: how are the prime numbers distributed among the positive integers? What is the number of prime numbers of 100 digits? Of 1,000 digits? These questions were the starting point of a groundbreaking paper by Bernhard Riemann written in 1859. As an aside in his article, Riemann formulated his now famous hypothesis that so far no one has come close to proving: All nontrivial zeroes of the zeta function lie on the critical line. Hidden behind this at first mysterious phrase lies a whole mathematical universe of prime numbers, infinite sequences, infinite products, and complex functions.

The present book is a first exploration of this fascinating, unknown world. It originated from an online course for mathematically talented secondary school students organized by the authors of this book at the University of Amsterdam. Its aim was to bring the students into contact with challenging university level mathematics and show them what the Riemann Hypothesis is all about and why it is such an important problem in mathematics.

• Chapters
• Chapter 1. Prime numbers
• Chapter 2. The zeta function
• Chapter 3. The Riemann hypothesis
• Chapter 4. Primes and the Riemann hypothesis
• Appendix A. Why big primes are useful
• Appendix B. Computer support
• Appendix C. Further reading and internet surfing
• Appendix D. Solutions to the exercises
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.