Skip to content
Cart 
Register Sign in Wishlist

Equivalents of the Riemann Hypothesis

Volume 1. Arithmetic Equivalents

AUD$165.41 exc GST

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: November 2017
  • availability: Available
  • format: Hardback
  • isbn: 9781107197046

AUD$ 165.41 exc GST
Hardback

Add to cart Add to wishlist

Other available formats:
eBook


Looking for an inspection copy?

Please email academicmarketing@cambridge.edu.au to enquire about an inspection copy of this book

Description
Product filter button
Description
Contents
Resources
Courses
About the Authors
  • The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

    • Gives students and researchers easy access to methods and results
    • Fully describes approaches to the Riemann hypothesis using arithmetic functions
    • Provides many unsolved problems suitable for research
    • Tailored software is freely available online
    Read more

    Reviews & endorsements

    'This two volume catalogue of many of the various equivalents of the Riemann Hypothesis by Kevin Broughan is a valuable addition to the literature … all in all these two volumes are a must have for anyone interested in the Riemann Hypothesis.' Steven Decke, MAA Reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity

    ×

    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?

    ×

    Product details

    • Date Published: November 2017
    • format: Hardback
    • isbn: 9781107197046
    • dimensions: 241 x 160 x 23 mm
    • weight: 0.65kg
    • contains: 52 b/w illus. 17 tables
    • availability: Available
  • Table of Contents

    1. Introduction
    2. The Riemann Zeta function
    3. Estimates
    4. Classical equivalences
    5. Euler's Totient function
    6. A variety of abundant numbers
    7. Robin's theorem
    8. Numbers which do not satisfy Robin's inequality
    9. Left, right and extremely abundant numbers
    10. Other equivalents to the Riemann hypothesis
    Appendix A. Tables
    Appendix B. RHpack mini-manual
    Bibliography
    Index.

  • Resources for

    Equivalents of the Riemann Hypothesis

    Kevin Broughan

    General Resources

    Find resources associated with this title

    Type Name Unlocked * Format Size

    Showing of

    Back to top

    This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

    Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

    Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

    If you are having problems accessing these resources please contact lecturers@cambridge.org.

  • Author

    Kevin Broughan, University of Waikato, New Zealand
    Kevin Broughan is Emeritus Professor in the Department of Mathematics and Statistics at the University of Waikato, New Zealand. In these two volumes he has used a unique combination of mathematical knowledge and skills. Following the publication of his Columbia University thesis, he worked on problems in topology before undertaking work on symbolic computation, leading to development of the software system SENAC. This led to a symbolic-numeric dynamical systems study of the zeta function, giving new insights into its behaviour, and was accompanied by publication of the software GL(n)pack as part of D. Goldfeld's book, Automorphic Forms and L-Functions for the Group GL(n,R). Professor Broughan has published widely on problems in prime number theory. His other achievements include co-establishing the New Zealand Mathematical Society, the School of Computing and Mathematical Sciences at the University of Waikato, and the basis for New Zealand's connection to the internet.

Sign In

Please sign in to access your account

Cancel

Not already registered? Create an account now. ×

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.

Cancel

Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

×
Please fill in the required fields in your feedback submission.
×