Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents
eBook - PDF

Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents

About this book

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.

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Yes, you can access Equivalents of the Riemann Hypothesis: Volume 1, Arithmetic Equivalents by Kevin Broughan in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half-title
  3. Series page
  4. Title page
  5. Copyright information
  6. Dedication1
  7. Epigraph
  8. Contents for Volume One
  9. Contents for Volume Two
  10. List of illustrations
  11. List of tables
  12. Preface
  13. Acknowledgements
  14. 1 Introduction
  15. 2 The Riemann Zeta Function
  16. 3 Estimates
  17. 4 Classical Equivalences
  18. 5 Euler's Totient Function
  19. 6 A Variety of Abundant Numbers
  20. 7 Robin's Theorem
  21. 8 Numbers That Do Not Satisfy Robin's Inequality
  22. 9 Left, Right and Extremely Abundant Numbers
  23. 10 Other Equivalents to the Riemann Hypothesis
  24. Appendix A Tables
  25. Appenix B RHpack Mini-Manual
  26. References
  27. Index